tomleslie

11832 Reputation

19 Badges

12 years, 136 days

MaplePrimes Activity


These are answers submitted by tomleslie

 - can't really see why you would want to do this

A couple of alternatives are shown in the attached

  restart;
  e:= a/b:
  f:= unapply(unapply(e, [indets(e, name)[]]), x);
  f(z)(A,B);
  g:= unapply(unapply(e, [indets(e, name)[]]));
  g()(A,B);
  h:= unapply(e, [indets(e, name)[]]);
  h(A,B);
  

proc (x) options operator, arrow; proc (a, b) options operator, arrow; a/b end proc end proc

 

A/B

 

proc () options operator, arrow; proc (a, b) options operator, arrow; a/b end proc end proc

 

A/B

 

proc (a, b) options operator, arrow; a/b end proc

 

A/B

(1)

 

Download oddProc2.mw

You have written

C[1, 1] = 0.0998238989835086492681507032141,

I assume you mean

C[1, 1](0) = 0.0998238989835086492681507032141

and the same for alll other initial conditions, in which case I get the attached which executes correctly

restart; with(plots)

sysM := [diff(C[1, 1](t), t) = -(3/16)*Pi*(C[2, 1](t)+4*C[1, 1](t)), diff(C[1, 2](t), t) = -5*Pi*(C[2, 2](t)+4*C[1, 2](t)), diff(C[1, 3](t), t) = -(945/4)*Pi*(C[2, 3](t)+4*C[1, 3](t)), diff(C[2, 1](t), t) = -(1/8)*Pi*(C[3, 1](t)+6*C[2, 1](t)+6*C[1, 1](t)), diff(C[2, 2](t), t) = -10.4719755119659774615421446110*C[3, 2](t)-62.8318530717958647692528676658*C[2, 2](t)-62.8318530717958647692528676658*C[1, 2](t)-2.38361014507273884349657421134*10^15*ZETA[1](t)*C[1, 1](t), diff(C[2, 3](t), t) = -494.800842940392435057866332869*C[3, 3](t)-2968.80505764235461034719799721*C[2, 3](t)-2968.80505764235461034719799721*C[1, 3](t)-1.35954060126371030332767566128*10^16*ZETA[1](t)*C[1, 2](t)-1.35954060126371030332767566128*10^16*ZETA[2](t)*C[1, 1](t), diff(C[3, 1](t), t) = -(3/8)*Pi*(2*C[3, 1](t)+3*C[2, 1](t)), diff(C[3, 2](t), t) = -62.8318530717958647692528676658*C[3, 2](t)-94.2477796076937971538793014986*C[2, 2](t)-1.12625579354686910355213131486*10^17*ZETA[1](t)*C[2, 1](t), diff(C[3, 3](t), t) = -2968.80505764235461034719799721*C[3, 3](t)-4453.20758646353191552079699581*C[2, 3](t)-6.42382934097103118322326749959*10^17*ZETA[1](t)*C[2, 2](t)-6.42382934097103118322326749959*10^17*ZETA[2](t)*C[2, 1](t), diff(ZETA[1](t), t) = -(1/3)*C[2, 1](t), diff(ZETA[2](t), t) = -(1/3)*C[2, 2](t), diff(ZETA[3](t), t) = -(1/3)*C[2, 3](t)]

ICS := [C[1, 1](0) = 0.998238989835086492681507032141e-1, C[1, 2](0) = -0.137051161872492529218951625903e-1, C[1, 3](0) = -0.629146365720807620696267926206e-2, C[2, 1](0) = 0.923300332435106257640735267282e-1, C[2, 2](0) = -0.126762613568515069966837491839e-1, C[2, 3](0) = -0.581915808273854734025727975244e-2, C[3, 1](0) = -0.190143920352772604950256237747e-1, C[3, 2](0) = 0.261054171122321128306306984717e-2, C[3, 3](0) = 0.119839394846335068333097530793e-2, ZETA[1](0) = .464598743230343884242076682299, ZETA[2](0) = .429720916976380440572769663279, ZETA[3](0) = -0.884964696113332752036741498040e-1]

sol := dsolve([sysM[], ICS[]], numeric)

proc (x_rkf45) local _res, _dat, _vars, _solnproc, _xout, _ndsol, _pars, _n, _i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; if 1 < nargs then error "invalid input: too many arguments" end if; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then _xout := evalf[_EnvDSNumericSaveDigits](x_rkf45) else _xout := evalf(x_rkf45) end if; _dat := Array(1..4, {(1) = proc (_xin) local _xout, _dtbl, _dat, _vmap, _x0, _y0, _val, _dig, _n, _ne, _nd, _nv, _pars, _ini, _par, _i, _j, _k, _src; option `Copyright (c) 2002 by Waterloo Maple Inc. All rights reserved.`; table( [( "complex" ) = false ] ) _xout := _xin; _pars := []; _dtbl := array( 1 .. 4, [( 1 ) = (array( 1 .. 28, [( 1 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 2 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 3 ) = ([0, 0, 0, Array(1..0, 1..2, {}, datatype = float[8], order = C_order)]), ( 4 ) = (Array(1..65, {(1) = 12, (2) = 12, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 1, (8) = 0, (9) = 0, (10) = 0, (11) = 0, (12) = 0, (13) = 0, (14) = 0, (15) = 0, (16) = 0, (17) = 0, (18) = 1, (19) = 30000, (20) = 0, (21) = 0, (22) = 1, (23) = 4, (24) = 0, (25) = 1, (26) = 15, (27) = 1, (28) = 0, (29) = 1, (30) = 3, (31) = 3, (32) = 0, (33) = 1, (34) = 0, (35) = 0, (36) = 0, (37) = 0, (38) = 0, (39) = 0, (40) = 0, (41) = 0, (42) = 0, (43) = 1, (44) = 0, (45) = 0, (46) = 0, (47) = 0, (48) = 0, (49) = 0, (50) = 50, (51) = 1, (52) = 0, (53) = 0, (54) = 0, (55) = 0, (56) = 0, (57) = 0, (58) = 0, (59) = 10000, (60) = 0, (61) = 1000, (62) = 0, (63) = 0, (64) = -1, (65) = 0}, datatype = integer[8])), ( 5 ) = (Array(1..28, {(1) = .0, (2) = 0.10e-5, (3) = .0, (4) = 0.500001e-14, (5) = .0, (6) = 0.2353547231998853e-18, (7) = .0, (8) = 0.10e-5, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = 1.0, (14) = .0, (15) = .49999999999999, (16) = .0, (17) = 1.0, (18) = 1.0, (19) = .0, (20) = .0, (21) = 1.0, (22) = 1.0, (23) = .0, (24) = .0, (25) = 0.10e-14, (26) = .0, (27) = .0, (28) = .0}, datatype = float[8], order = C_order)), ( 6 ) = (Array(1..12, {(1) = 0.998238989835086e-1, (2) = -0.137051161872493e-1, (3) = -0.629146365720808e-2, (4) = 0.923300332435106e-1, (5) = -0.126762613568515e-1, (6) = -0.581915808273855e-2, (7) = -0.190143920352773e-1, (8) = 0.261054171122321e-2, (9) = 0.119839394846335e-2, (10) = .464598743230344, (11) = .42972091697638, (12) = -0.884964696113333e-1}, datatype = float[8], order = C_order)), ( 7 ) = ([Array(1..4, 1..7, {(1, 1) = .0, (1, 2) = .203125, (1, 3) = .3046875, (1, 4) = .75, (1, 5) = .8125, (1, 6) = .40625, (1, 7) = .8125, (2, 1) = 0.6378173828125e-1, (2, 2) = .0, (2, 3) = .279296875, (2, 4) = .27237892150878906, (2, 5) = -0.9686851501464844e-1, (2, 6) = 0.1956939697265625e-1, (2, 7) = .5381584167480469, (3, 1) = 0.31890869140625e-1, (3, 2) = .0, (3, 3) = -.34375, (3, 4) = -.335235595703125, (3, 5) = .2296142578125, (3, 6) = .41748046875, (3, 7) = 11.480712890625, (4, 1) = 0.9710520505905151e-1, (4, 2) = .0, (4, 3) = .40350341796875, (4, 4) = 0.20297467708587646e-1, (4, 5) = -0.6054282188415527e-2, (4, 6) = -0.4770040512084961e-1, (4, 7) = .77858567237854}, datatype = float[8], order = C_order), Array(1..6, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = 1.0, (2, 1) = .25, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = 1.0, (3, 1) = .1875, (3, 2) = .5625, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = 2.0, (4, 1) = .23583984375, (4, 2) = -.87890625, (4, 3) = .890625, (4, 4) = .0, (4, 5) = .0, (4, 6) = .2681884765625, (5, 1) = .1272735595703125, (5, 2) = -.5009765625, (5, 3) = .44921875, (5, 4) = -0.128936767578125e-1, (5, 5) = .0, (5, 6) = 0.626220703125e-1, (6, 1) = -0.927734375e-1, (6, 2) = .626220703125, (6, 3) = -.4326171875, (6, 4) = .1418304443359375, (6, 5) = -0.861053466796875e-1, (6, 6) = .3131103515625}, datatype = float[8], order = C_order), Array(1..6, {(1) = .0, (2) = .386, (3) = .21, (4) = .63, (5) = 1.0, (6) = 1.0}, datatype = float[8], order = C_order), Array(1..6, {(1) = .25, (2) = -.1043, (3) = .1035, (4) = -0.362e-1, (5) = .0, (6) = .0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 1.544, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = .9466785280815533, (3, 2) = .25570116989825814, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = 3.3148251870684886, (4, 2) = 2.896124015972123, (4, 3) = .9986419139977808, (4, 4) = .0, (4, 5) = .0, (5, 1) = 1.2212245092262748, (5, 2) = 6.019134481287752, (5, 3) = 12.537083329320874, (5, 4) = -.687886036105895, (5, 5) = .0, (6, 1) = 1.2212245092262748, (6, 2) = 6.019134481287752, (6, 3) = 12.537083329320874, (6, 4) = -.687886036105895, (6, 5) = 1.0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = -5.6688, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = -2.4300933568337584, (3, 2) = -.20635991570891224, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = -.10735290581452621, (4, 2) = -9.594562251021896, (4, 3) = -20.470286148096154, (4, 4) = .0, (4, 5) = .0, (5, 1) = 7.496443313968615, (5, 2) = -10.246804314641219, (5, 3) = -33.99990352819906, (5, 4) = 11.708908932061595, (5, 5) = .0, (6, 1) = 8.083246795922411, (6, 2) = -7.981132988062785, (6, 3) = -31.52159432874373, (6, 4) = 16.319305431231363, (6, 5) = -6.0588182388340535}, datatype = float[8], order = C_order), Array(1..3, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 10.126235083446911, (2, 2) = -7.487995877607633, (2, 3) = -34.800918615557414, (2, 4) = -7.9927717075687275, (2, 5) = 1.0251377232956207, (3, 1) = -.6762803392806898, (3, 2) = 6.087714651678606, (3, 3) = 16.43084320892463, (3, 4) = 24.767225114183653, (3, 5) = -6.5943891257167815}, datatype = float[8], order = C_order)]), ( 9 ) = ([Array(1..12, {(1) = .1, (2) = .1, (3) = .1, (4) = .1, (5) = .1, (6) = .1, (7) = .1, (8) = .1, (9) = .1, (10) = .1, (11) = .1, (12) = .1}, datatype = float[8], order = C_order), Array(1..12, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0}, datatype = float[8], order = C_order), Array(1..12, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0}, datatype = float[8], order = C_order), Array(1..12, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0}, datatype = float[8], order = C_order), Array(1..12, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0}, datatype = float[8], order = C_order), Array(1..12, 1..12, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .0, (1, 9) = .0, (1, 10) = .0, (1, 11) = .0, (1, 12) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (2, 8) = .0, (2, 9) = .0, (2, 10) = .0, (2, 11) = .0, (2, 12) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (3, 8) = .0, (3, 9) = .0, (3, 10) = .0, (3, 11) = .0, (3, 12) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (4, 8) = .0, (4, 9) = .0, (4, 10) = .0, (4, 11) = .0, (4, 12) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (5, 8) = .0, (5, 9) = .0, (5, 10) = .0, (5, 11) = .0, (5, 12) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (6, 8) = .0, (6, 9) = .0, (6, 10) = .0, (6, 11) = .0, (6, 12) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (7, 7) = .0, (7, 8) = .0, (7, 9) = .0, (7, 10) = .0, (7, 11) = .0, (7, 12) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (8, 7) = .0, (8, 8) = .0, (8, 9) = .0, (8, 10) = .0, (8, 11) = .0, (8, 12) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (9, 7) = .0, (9, 8) = .0, (9, 9) = .0, (9, 10) = .0, (9, 11) = .0, (9, 12) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (10, 7) = .0, (10, 8) = .0, (10, 9) = .0, (10, 10) = .0, (10, 11) = .0, (10, 12) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (11, 7) = .0, (11, 8) = .0, (11, 9) = .0, (11, 10) = .0, (11, 11) = .0, (11, 12) = .0, (12, 1) = .0, (12, 2) = .0, (12, 3) = .0, (12, 4) = .0, (12, 5) = .0, (12, 6) = .0, (12, 7) = .0, (12, 8) = .0, (12, 9) = .0, (12, 10) = .0, (12, 11) = .0, (12, 12) = .0}, datatype = float[8], order = C_order), Array(1..12, 1..12, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .0, (1, 9) = .0, (1, 10) = .0, (1, 11) = .0, (1, 12) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (2, 8) = .0, (2, 9) = .0, (2, 10) = .0, (2, 11) = .0, (2, 12) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (3, 8) = .0, (3, 9) = .0, (3, 10) = .0, (3, 11) = .0, (3, 12) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (4, 8) = .0, (4, 9) = .0, (4, 10) = .0, (4, 11) = .0, (4, 12) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (5, 8) = .0, (5, 9) = .0, (5, 10) = .0, (5, 11) = .0, (5, 12) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (6, 8) = .0, (6, 9) = .0, (6, 10) = .0, (6, 11) = .0, (6, 12) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (7, 7) = .0, (7, 8) = .0, (7, 9) = .0, (7, 10) = .0, (7, 11) = .0, (7, 12) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (8, 7) = .0, (8, 8) = .0, (8, 9) = .0, (8, 10) = .0, (8, 11) = .0, (8, 12) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (9, 7) = .0, (9, 8) = .0, (9, 9) = .0, (9, 10) = .0, (9, 11) = .0, (9, 12) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (10, 7) = .0, (10, 8) = .0, (10, 9) = .0, (10, 10) = .0, (10, 11) = .0, (10, 12) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (11, 7) = .0, (11, 8) = .0, (11, 9) = .0, (11, 10) = .0, (11, 11) = .0, (11, 12) = .0, (12, 1) = .0, (12, 2) = .0, (12, 3) = .0, (12, 4) = .0, (12, 5) = .0, (12, 6) = .0, (12, 7) = .0, (12, 8) = .0, (12, 9) = .0, (12, 10) = .0, (12, 11) = .0, (12, 12) = .0}, datatype = float[8], order = C_order), Array(1..12, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0}, datatype = float[8], order = C_order), Array(1..12, 1..12, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .0, (1, 9) = .0, (1, 10) = .0, (1, 11) = .0, (1, 12) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (2, 8) = .0, (2, 9) = .0, (2, 10) = .0, (2, 11) = .0, (2, 12) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (3, 8) = .0, (3, 9) = .0, (3, 10) = .0, (3, 11) = .0, (3, 12) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (4, 8) = .0, (4, 9) = .0, (4, 10) = .0, (4, 11) = .0, (4, 12) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (5, 8) = .0, (5, 9) = .0, (5, 10) = .0, (5, 11) = .0, (5, 12) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (6, 8) = .0, (6, 9) = .0, (6, 10) = .0, (6, 11) = .0, (6, 12) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (7, 7) = .0, (7, 8) = .0, (7, 9) = .0, (7, 10) = .0, (7, 11) = .0, (7, 12) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (8, 7) = .0, (8, 8) = .0, (8, 9) = .0, (8, 10) = .0, (8, 11) = .0, (8, 12) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (9, 7) = .0, (9, 8) = .0, (9, 9) = .0, (9, 10) = .0, (9, 11) = .0, (9, 12) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (10, 7) = .0, (10, 8) = .0, (10, 9) = .0, (10, 10) = .0, (10, 11) = .0, (10, 12) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (11, 7) = .0, (11, 8) = .0, (11, 9) = .0, (11, 10) = .0, (11, 11) = .0, (11, 12) = .0, (12, 1) = .0, (12, 2) = .0, (12, 3) = .0, (12, 4) = .0, (12, 5) = .0, (12, 6) = .0, (12, 7) = .0, (12, 8) = .0, (12, 9) = .0, (12, 10) = .0, (12, 11) = .0, (12, 12) = .0}, datatype = float[8], order = C_order), Array(1..12, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (12, 1) = .0, (12, 2) = .0, (12, 3) = .0, (12, 4) = .0, (12, 5) = .0, (12, 6) = .0}, datatype = float[8], order = C_order), Array(1..12, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 0, (8) = 0, (9) = 0, (10) = 0, (11) = 0, (12) = 0}, datatype = integer[8]), Array(1..12, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0}, datatype = float[8], order = C_order), Array(1..12, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0}, datatype = float[8], order = C_order), Array(1..12, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0}, datatype = float[8], order = C_order), Array(1..12, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0}, datatype = float[8], order = C_order), Array(1..12, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0}, datatype = float[8], order = C_order), Array(1..24, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0, (22) = .0, (23) = .0, (24) = .0}, datatype = float[8], order = C_order), Array(1..12, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 0, (8) = 0, (9) = 0, (10) = 0, (11) = 0, (12) = 0}, datatype = integer[8])]), ( 8 ) = ([Array(1..12, {(1) = 0.998238989835086e-1, (2) = -0.137051161872493e-1, (3) = -0.629146365720808e-2, (4) = 0.923300332435106e-1, (5) = -0.126762613568515e-1, (6) = -0.581915808273855e-2, (7) = -0.190143920352773e-1, (8) = 0.261054171122321e-2, (9) = 0.119839394846335e-2, (10) = .464598743230344, (11) = .42972091697638, (12) = -0.884964696113333e-1}, datatype = float[8], order = C_order), Array(1..12, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0}, datatype = float[8], order = C_order), Array(1..12, {(1) = -.2895913996763696, (2) = 1.0602360943774856, (3) = 22.997115612306096, (4) = -.44528510209078204, (5) = -110547209583016.8, (6) = -496627098018920.7, (7) = -.28151966766357545, (8) = -4831233864687141., (9) = -21704045380777476., (10) = -0.30776677747836868e-1, (11) = 0.42254204522838325e-2, (12) = 0.19397193609128499e-2}, datatype = float[8], order = C_order), 0, 0]), ( 11 ) = (Array(1..6, 0..12, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .0, (1, 9) = .0, (1, 10) = .0, (1, 11) = .0, (1, 12) = .0, (2, 0) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (2, 8) = .0, (2, 9) = .0, (2, 10) = .0, (2, 11) = .0, (2, 12) = .0, (3, 0) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (3, 8) = .0, (3, 9) = .0, (3, 10) = .0, (3, 11) = .0, (3, 12) = .0, (4, 0) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (4, 8) = .0, (4, 9) = .0, (4, 10) = .0, (4, 11) = .0, (4, 12) = .0, (5, 0) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (5, 8) = .0, (5, 9) = .0, (5, 10) = .0, (5, 11) = .0, (5, 12) = .0, (6, 0) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (6, 8) = .0, (6, 9) = .0, (6, 10) = .0, (6, 11) = .0, (6, 12) = .0}, datatype = float[8], order = C_order)), ( 10 ) = ([proc (N, X, Y, YP) option `[Y[1] = C[1,1](t), Y[2] = C[1,2](t), Y[3] = C[1,3](t), Y[4] = C[2,1](t), Y[5] = C[2,2](t), Y[6] = C[2,3](t), Y[7] = C[3,1](t), Y[8] = C[3,2](t), Y[9] = C[3,3](t), Y[10] = ZETA[1](t), Y[11] = ZETA[2](t), Y[12] = ZETA[3](t)]`; YP[1] := -.589048622548086*Y[4]-2.35619449019235*Y[1]; YP[2] := -15.7079632679490*Y[5]-62.8318530717960*Y[2]; YP[3] := -742.201264410588*Y[6]-2968.80505764236*Y[3]; YP[4] := -.392699081698724*Y[7]-2.35619449019234*Y[4]-2.35619449019234*Y[1]; YP[5] := -10.4719755119659774615421446110*Y[8]-62.8318530717958647692528676658*Y[5]-62.8318530717958647692528676658*Y[2]-0.2383610145e16*Y[10]*Y[1]; YP[6] := -494.800842940392435057866332869*Y[9]-2968.80505764235461034719799721*Y[6]-2968.80505764235461034719799721*Y[3]-0.1359540601e17*Y[10]*Y[2]-0.1359540601e17*Y[11]*Y[1]; YP[7] := -2.35619449019234*Y[7]-3.53429173528851*Y[4]; YP[8] := -62.8318530717958647692528676658*Y[8]-94.2477796076937971538793014986*Y[5]-0.1126255794e18*Y[10]*Y[4]; YP[9] := -2968.80505764235461034719799721*Y[9]-4453.20758646353191552079699581*Y[6]-0.6423829341e18*Y[10]*Y[5]-0.6423829341e18*Y[11]*Y[4]; YP[10] := -(1/3)*Y[4]; YP[11] := -(1/3)*Y[5]; YP[12] := -(1/3)*Y[6]; 0 end proc, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]), ( 13 ) = (), ( 12 ) = (), ( 15 ) = ("rkf45"), ( 14 ) = ([0, 0]), ( 18 ) = ([]), ( 19 ) = (0), ( 16 ) = ([0, 0, 0, 0, 0, []]), ( 17 ) = ([proc (N, X, Y, YP) option `[Y[1] = C[1,1](t), Y[2] = C[1,2](t), Y[3] = C[1,3](t), Y[4] = C[2,1](t), Y[5] = C[2,2](t), Y[6] = C[2,3](t), Y[7] = C[3,1](t), Y[8] = C[3,2](t), Y[9] = C[3,3](t), Y[10] = ZETA[1](t), Y[11] = ZETA[2](t), Y[12] = ZETA[3](t)]`; YP[1] := -.589048622548086*Y[4]-2.35619449019235*Y[1]; YP[2] := -15.7079632679490*Y[5]-62.8318530717960*Y[2]; YP[3] := -742.201264410588*Y[6]-2968.80505764236*Y[3]; YP[4] := -.392699081698724*Y[7]-2.35619449019234*Y[4]-2.35619449019234*Y[1]; YP[5] := -10.4719755119659774615421446110*Y[8]-62.8318530717958647692528676658*Y[5]-62.8318530717958647692528676658*Y[2]-0.2383610145e16*Y[10]*Y[1]; YP[6] := -494.800842940392435057866332869*Y[9]-2968.80505764235461034719799721*Y[6]-2968.80505764235461034719799721*Y[3]-0.1359540601e17*Y[10]*Y[2]-0.1359540601e17*Y[11]*Y[1]; YP[7] := -2.35619449019234*Y[7]-3.53429173528851*Y[4]; YP[8] := -62.8318530717958647692528676658*Y[8]-94.2477796076937971538793014986*Y[5]-0.1126255794e18*Y[10]*Y[4]; YP[9] := -2968.80505764235461034719799721*Y[9]-4453.20758646353191552079699581*Y[6]-0.6423829341e18*Y[10]*Y[5]-0.6423829341e18*Y[11]*Y[4]; YP[10] := -(1/3)*Y[4]; YP[11] := -(1/3)*Y[5]; YP[12] := -(1/3)*Y[6]; 0 end proc, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]), ( 22 ) = (0), ( 23 ) = (0), ( 20 ) = ([]), ( 21 ) = (0), ( 27 ) = (""), ( 26 ) = (Array(1..0, {})), ( 25 ) = (Array(1..0, {})), ( 24 ) = (0), ( 28 ) = (0)  ] ))  ] ); _y0 := Array(0..12, {(1) = 0., (2) = 0.998238989835086e-1, (3) = -0.137051161872493e-1, (4) = -0.629146365720808e-2, (5) = 0.923300332435106e-1, (6) = -0.126762613568515e-1, (7) = -0.581915808273855e-2, (8) = -0.190143920352773e-1, (9) = 0.261054171122321e-2, (10) = 0.119839394846335e-2, (11) = .464598743230344, (12) = .429720916976380}); _vmap := array( 1 .. 12, [( 1 ) = (1), ( 2 ) = (2), ( 3 ) = (3), ( 4 ) = (4), ( 5 ) = (5), ( 6 ) = (6), ( 7 ) = (7), ( 9 ) = (9), ( 8 ) = (8), ( 11 ) = (11), ( 10 ) = (10), ( 12 ) = (12)  ] ); _x0 := _dtbl[1][5][5]; _n := _dtbl[1][4][1]; _ne := _dtbl[1][4][3]; _nd := _dtbl[1][4][4]; _nv := _dtbl[1][4][16]; if not type(_xout, 'numeric') then if member(_xout, ["start", "left", "right"]) then if _Env_smart_dsolve_numeric = true or _dtbl[1][4][10] = 1 then if _xout = "left" then if type(_dtbl[2], 'table') then return _dtbl[2][5][1] end if elif _xout = "right" then if type(_dtbl[3], 'table') then return _dtbl[3][5][1] end if end if end if; return _dtbl[1][5][5] elif _xout = "method" then return _dtbl[1][15] elif _xout = "storage" then return evalb(_dtbl[1][4][10] = 1) elif _xout = "leftdata" then if not type(_dtbl[2], 'array') then return NULL else return eval(_dtbl[2]) end if elif _xout = "rightdata" then if not type(_dtbl[3], 'array') then return NULL else return eval(_dtbl[3]) end if elif _xout = "enginedata" then return eval(_dtbl[1]) elif _xout = "enginereset" then _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); return NULL elif _xout = "initial" then return procname(_y0[0]) elif _xout = "laxtol" then return _dtbl[`if`(member(_dtbl[4], {2, 3}), _dtbl[4], 1)][5][18] elif _xout = "numfun" then return `if`(member(_dtbl[4], {2, 3}), _dtbl[_dtbl[4]][4][18], 0) elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return procname(_y0[0]), [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "last" then if _dtbl[4] <> 2 and _dtbl[4] <> 3 or _x0-_dtbl[_dtbl[4]][5][1] = 0. then error "no information is available on last computed point" else _xout := _dtbl[_dtbl[4]][5][1] end if elif _xout = "function" then if _dtbl[1][4][33]-2. = 0 then return eval(_dtbl[1][10], 1) else return eval(_dtbl[1][10][1], 1) end if elif _xout = "map" then return copy(_vmap) elif type(_xin, `=`) and type(rhs(_xin), 'list') and member(lhs(_xin), {"initial", "parameters", "initial_and_parameters"}) then _ini, _par := [], []; if lhs(_xin) = "initial" then _ini := rhs(_xin) elif lhs(_xin) = "parameters" then _par := rhs(_xin) elif select(type, rhs(_xin), `=`) <> [] then _par, _ini := selectremove(type, rhs(_xin), `=`) elif nops(rhs(_xin)) < nops(_pars)+1 then error "insufficient data for specification of initial and parameters" else _par := rhs(_xin)[-nops(_pars) .. -1]; _ini := rhs(_xin)[1 .. -nops(_pars)-1] end if; _xout := lhs(_xout); _i := false; if _par <> [] then _i := `dsolve/numeric/process_parameters`(_n, _pars, _par, _y0) end if; if _ini <> [] then _i := `dsolve/numeric/process_initial`(_n-_ne, _ini, _y0, _pars, _vmap) or _i end if; if _i then `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars); if _Env_smart_dsolve_numeric = true and type(_y0[0], 'numeric') and _dtbl[1][4][10] <> 1 then procname("right") := _y0[0]; procname("left") := _y0[0] end if end if; if _xout = "initial" then return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)] elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] else return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)], [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] end if elif _xin = "eventstop" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then return 0 end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 100 and 100 <= _dtbl[5-_i][4][9] then _i := 5-_i; _dtbl[4] := _i; _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) elif 100 <= _dtbl[_i][4][9] then _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) else return 0 end if elif _xin = "eventstatus" then if _nv = 0 then error "this solution has no events" end if; _i := [selectremove(proc (a) options operator, arrow; _dtbl[1][3][1][a, 7] = 1 end proc, {seq(_j, _j = 1 .. round(_dtbl[1][3][1][_nv+1, 1]))})]; return ':-enabled' = _i[1], ':-disabled' = _i[2] elif _xin = "eventclear" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then error "no events to clear" end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 100 and 100 < _dtbl[5-_i][4][9] then _dtbl[4] := 5-_i; _i := 5-_i end if; if _dtbl[_i][4][9] < 100 then error "no events to clear" elif _nv < _dtbl[_i][4][9]-100 then error "event error condition cannot be cleared" else _j := _dtbl[_i][4][9]-100; if irem(round(_dtbl[_i][3][1][_j, 4]), 2) = 1 then error "retriggerable events cannot be cleared" end if; _j := round(_dtbl[_i][3][1][_j, 1]); for _k to _nv do if _dtbl[_i][3][1][_k, 1] = _j then if _dtbl[_i][3][1][_k, 2] = 3 then error "range events cannot be cleared" end if; _dtbl[_i][3][1][_k, 8] := _dtbl[_i][3][1][_nv+1, 8] end if end do; _dtbl[_i][4][17] := 0; _dtbl[_i][4][9] := 0; if _dtbl[1][4][10] = 1 then if _i = 2 then try procname(procname("left")) catch:  end try else try procname(procname("right")) catch:  end try end if end if end if; return  elif type(_xin, `=`) and member(lhs(_xin), {"eventdisable", "eventenable"}) then if _nv = 0 then error "this solution has no events" end if; if type(rhs(_xin), {('list')('posint'), ('set')('posint')}) then _i := {op(rhs(_xin))} elif type(rhs(_xin), 'posint') then _i := {rhs(_xin)} else error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; if select(proc (a) options operator, arrow; _nv < a end proc, _i) <> {} then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _k := {}; for _j to _nv do if member(round(_dtbl[1][3][1][_j, 1]), _i) then _k := `union`(_k, {_j}) end if end do; _i := _k; if lhs(_xin) = "eventdisable" then _dtbl[4] := 0; _j := [evalb(assigned(_dtbl[2]) and member(_dtbl[2][4][17], _i)), evalb(assigned(_dtbl[3]) and member(_dtbl[3][4][17], _i))]; for _k in _i do _dtbl[1][3][1][_k, 7] := 0; if assigned(_dtbl[2]) then _dtbl[2][3][1][_k, 7] := 0 end if; if assigned(_dtbl[3]) then _dtbl[3][3][1][_k, 7] := 0 end if end do; if _j[1] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[2][3][4][_k, 1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to defined init `, _dtbl[2][3][4][_k, 1]); _dtbl[2][3][1][_k, 8] := _dtbl[2][3][4][_k, 1] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to rate hysteresis init `, _dtbl[2][5][24]); _dtbl[2][3][1][_k, 8] := _dtbl[2][5][24] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to initial init `, _x0); _dtbl[2][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to fireinitial init `, _x0-1); _dtbl[2][3][1][_k, 8] := _x0-1 end if end do; _dtbl[2][4][17] := 0; _dtbl[2][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("left")) end if end if; if _j[2] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[3][3][4][_k, 2], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to defined init `, _dtbl[3][3][4][_k, 2]); _dtbl[3][3][1][_k, 8] := _dtbl[3][3][4][_k, 2] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to rate hysteresis init `, _dtbl[3][5][24]); _dtbl[3][3][1][_k, 8] := _dtbl[3][5][24] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to initial init `, _x0); _dtbl[3][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to fireinitial init `, _x0+1); _dtbl[3][3][1][_k, 8] := _x0+1 end if end do; _dtbl[3][4][17] := 0; _dtbl[3][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("right")) end if end if else for _k in _i do _dtbl[1][3][1][_k, 7] := 1 end do; _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); _dtbl[4] := 0; if _dtbl[1][4][10] = 1 then if _x0 <= procname("right") then try procname(procname("right")) catch:  end try end if; if procname("left") <= _x0 then try procname(procname("left")) catch:  end try end if end if end if; return  elif type(_xin, `=`) and lhs(_xin) = "eventfired" then if not type(rhs(_xin), 'list') then error "'eventfired' must be specified as a list" end if; if _nv = 0 then error "this solution has no events" end if; if _dtbl[4] <> 2 and _dtbl[4] <> 3 then error "'direction' must be set prior to calling/setting 'eventfired'" end if; _i := _dtbl[4]; _val := NULL; if not assigned(_EnvEventRetriggerWarned) then _EnvEventRetriggerWarned := false end if; for _k in rhs(_xin) do if type(_k, 'integer') then _src := _k elif type(_k, 'integer' = 'anything') and type(evalf(rhs(_k)), 'numeric') then _k := lhs(_k) = evalf[max(Digits, 18)](rhs(_k)); _src := lhs(_k) else error "'eventfired' entry is not valid: %1", _k end if; if _src < 1 or round(_dtbl[1][3][1][_nv+1, 1]) < _src then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _src := {seq(`if`(_dtbl[1][3][1][_j, 1]-_src = 0., _j, NULL), _j = 1 .. _nv)}; if nops(_src) <> 1 then error "'eventfired' can only be set/queried for root-finding events and time/interval events" end if; _src := _src[1]; if _dtbl[1][3][1][_src, 2] <> 0. and _dtbl[1][3][1][_src, 2]-2. <> 0. then error "'eventfired' can only be set/queried for root-finding events and time/interval events" elif irem(round(_dtbl[1][3][1][_src, 4]), 2) = 1 then if _EnvEventRetriggerWarned = false then WARNING(`'eventfired' has no effect on events that retrigger`) end if; _EnvEventRetriggerWarned := true end if; if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then _val := _val, undefined elif type(_dtbl[_i][3][4][_src, _i-1], 'undefined') or _i = 2 and _dtbl[2][3][1][_src, 8] < _dtbl[2][3][4][_src, 1] or _i = 3 and _dtbl[3][3][4][_src, 2] < _dtbl[3][3][1][_src, 8] then _val := _val, _dtbl[_i][3][1][_src, 8] else _val := _val, _dtbl[_i][3][4][_src, _i-1] end if; if type(_k, `=`) then if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then error "cannot set event code for a rate hysteresis event" end if; userinfo(3, {'events', 'eventreset'}, `manual set event code `, _src, ` to value `, rhs(_k)); _dtbl[_i][3][1][_src, 8] := rhs(_k); _dtbl[_i][3][4][_src, _i-1] := rhs(_k) end if end do; return [_val] elif type(_xin, `=`) and lhs(_xin) = "direction" then if not member(rhs(_xin), {-1, 1, ':-left', ':-right'}) then error "'direction' must be specified as either '1' or 'right' (positive) or '-1' or 'left' (negative)" end if; _src := `if`(_dtbl[4] = 2, -1, `if`(_dtbl[4] = 3, 1, undefined)); _i := `if`(member(rhs(_xin), {1, ':-right'}), 3, 2); _dtbl[4] := _i; _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if; return _src elif _xin = "eventcount" then if _dtbl[1][3][1] = 0 or _dtbl[4] <> 2 and _dtbl[4] <> 3 then return 0 else return round(_dtbl[_dtbl[4]][3][1][_nv+1, 12]) end if elif type(_xin, `=`) and lhs(_xin) = "setdatacallback" then if not type(rhs(_xin), 'nonegint') then error "data callback must be a nonnegative integer (address)" end if; _dtbl[1][28] := rhs(_xin) else return "procname" end if end if; if _xout = _x0 then return [_x0, seq(evalf(_dtbl[1][6][_vmap[_i]]), _i = 1 .. _n-_ne)] end if; _i := `if`(_x0 <= _xout, 3, 2); if _xin = "last" and 0 < _dtbl[_i][4][9] and _dtbl[_i][4][9] < 100 then _dat := eval(_dtbl[_i], 2); _j := _dat[4][20]; return [_dat[11][_j, 0], seq(_dat[11][_j, _vmap[_i]], _i = 1 .. _n-_ne-_nd), seq(_dat[8][1][_vmap[_i]], _i = _n-_ne-_nd+1 .. _n-_ne)] end if; if not type(_dtbl[_i], 'array') then _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if end if; if _xin <> "last" then if 0 < 0 then if `dsolve/numeric/checkglobals`(op(_dtbl[1][14]), _pars, _n, _y0) then `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars, _i) end if end if; if _dtbl[1][4][7] = 0 then error "parameters must be initialized before solution can be computed" end if end if; _dat := eval(_dtbl[_i], 2); _dtbl[4] := _i; try _src := `dsolve/numeric/SC/IVPrun`(_dat, _xout) catch: userinfo(2, `dsolve/debug`, print(`Exception in solnproc:`, [lastexception][2 .. -1])); error  end try; if _dat[17] <> _dtbl[1][17] then _dtbl[1][17] := _dat[17]; _dtbl[1][10] := _dat[10] end if; if _src = 0 and 100 < _dat[4][9] then _val := _dat[3][1][_nv+1, 8] else _val := _dat[11][_dat[4][20], 0] end if; if _src <> 0 or _dat[4][9] <= 0 then _dtbl[1][5][1] := _xout else _dtbl[1][5][1] := _val end if; if _i = 3 and _val < _xout then Rounding := -infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further right of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further right of %1, maxfun limit exceeded (see ?dsolve,maxfun for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further right of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further right of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif _dat[4][9] = 6 then error "cannot evaluate the solution further right of %1, cannot downgrade delay storage for problems with delay derivative order > 1, try increasing delaypts", evalf[8](_val) elif _dat[4][9] = 10 then error "cannot evaluate the solution further right of %1, interrupt requested", evalf[8](_val) elif 100 < _dat[4][9] then if _dat[4][9]-100 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further right of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-100, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further right of %1", evalf[8](_val) end if elif _i = 2 and _xout < _val then Rounding := infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further left of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further left of %1, maxfun limit exceeded (see ?dsolve,maxfun for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further left of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further left of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif _dat[4][9] = 6 then error "cannot evaluate the solution further left of %1, cannot downgrade delay storage for problems with delay derivative order > 1, try increasing delaypts", evalf[8](_val) elif _dat[4][9] = 10 then error "cannot evaluate the solution further right of %1, interrupt requested", evalf[8](_val) elif 100 < _dat[4][9] then if _dat[4][9]-100 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further left of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-100, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further left of %1", evalf[8](_val) end if end if; if _EnvInFsolve = true then _dig := _dat[4][26]; if type(_EnvDSNumericSaveDigits, 'posint') then _dat[4][26] := _EnvDSNumericSaveDigits else _dat[4][26] := Digits end if; _Env_dsolve_SC_native := true; if _dat[4][25] = 1 then _i := 1; _dat[4][25] := 2 else _i := _dat[4][25] end if; _val := `dsolve/numeric/SC/IVPval`(_dat, _xout, _src); _dat[4][25] := _i; _dat[4][26] := _dig; [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] else Digits := _dat[4][26]; _val := `dsolve/numeric/SC/IVPval`(eval(_dat, 2), _xout, _src); [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] end if end proc, (2) = Array(0..0, {}), (3) = [t, C[1, 1](t), C[1, 2](t), C[1, 3](t), C[2, 1](t), C[2, 2](t), C[2, 3](t), C[3, 1](t), C[3, 2](t), C[3, 3](t), ZETA[1](t), ZETA[2](t), ZETA[3](t)], (4) = []}); _vars := _dat[3]; _pars := map(rhs, _dat[4]); _n := nops(_vars)-1; _solnproc := _dat[1]; if not type(_xout, 'numeric') then if member(x_rkf45, ["start", 'start', "method", 'method', "left", 'left', "right", 'right', "leftdata", "rightdata", "enginedata", "eventstop", 'eventstop', "eventclear", 'eventclear', "eventstatus", 'eventstatus', "eventcount", 'eventcount', "laxtol", 'laxtol', "numfun", 'numfun', NULL]) then _res := _solnproc(convert(x_rkf45, 'string')); if 1 < nops([_res]) then return _res elif type(_res, 'array') then return eval(_res, 1) elif _res <> "procname" then return _res end if elif member(x_rkf45, ["last", 'last', "initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(x_rkf45, 'string'); _res := _solnproc(_xout); if _xout = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] end if elif type(_xout, `=`) and member(lhs(_xout), ["initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(lhs(x_rkf45), 'string') = rhs(x_rkf45); if type(rhs(_xout), 'list') then _res := _solnproc(_xout) else error "initial and/or parameter values must be specified in a list" end if; if lhs(_xout) = "initial" then return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] elif lhs(_xout) = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] end if elif type(_xout, `=`) and member(lhs(_xout), ["eventdisable", 'eventdisable', "eventenable", 'eventenable', "eventfired", 'eventfired', "direction", 'direction', NULL]) then return _solnproc(convert(lhs(x_rkf45), 'string') = rhs(x_rkf45)) elif _xout = "solnprocedure" then return eval(_solnproc) elif _xout = "sysvars" then return _vars end if; if procname <> unknown then return ('procname')(x_rkf45) else _ndsol := 1; _ndsol := _ndsol; _ndsol := pointto(_dat[2][0]); return ('_ndsol')(x_rkf45) end if end if; try _res := _solnproc(_xout); [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] catch: error  end try end proc

(1)

odeplot(sol, [[t, C[1, 1](t)], [t, C[1, 2](t)], [t, C[1, 3](t)], [t, C[2, 1](t)], [t, C[2, 2](t)], [t, C[2, 3](t)], [t, C[3, 1](t)], [t, C[3, 2](t)], [t, C[3, 3](t)], [t, ZETA[1](t)], [t, ZETA[2](t)], [t, ZETA[3](t)]], t = 0 .. 2)

 

 

Download bigODE.mw

I just downloaded the latest Physics Updates for Maple 2022, and your problem is solved - see the atached

NB I am aware  that you specified Maple 2021: I'm guesing that the lalest Physics updates *may* not work with that release

Attempt to solve with Heaviside

restart;
interface(version);
Physics:-Version();

`Standard Worksheet Interface, Maple 2022.1, Windows 7, May 26 2022 Build ID 1619613`

 

`The "Physics Updates" version in the MapleCloud is 1257 and is the same as the version installed in this computer, created 2022, June 22, 16:27 hours Pacific Time.`

(1)

de := diff(u(x),x$2) = Heaviside(x - a)*u(x);

diff(diff(u(x), x), x) = Heaviside(x-a)*u(x)

(2)

dsolve fails:

dsolve(de);

u(x) = DESol({diff(diff(_Y(x), x), x)-Heaviside(x-a)*_Y(x)}, {_Y(x)})

(3)

Attempt to solve with piecewise

restart;

de := diff(u(x),x$2) = piecewise(x < a, 0, 1)*u(x);

de := diff(u(x), x, x) = piecewise(x < a, 0, 1)*u(x)

(4)

dsolve(de);

u(x) = piecewise(x < a, _C1*x+_C2, a <= x, ((1/2)*(a-1)*exp(a-x)+(1/2)*(a+1)*exp(x-a))*_C1+((1/2)*exp(a-x)+(1/2)*exp(x-a))*_C2)

(5)

dsolve(de, u(x));

u(x) = piecewise(x < a, _C1*x+_C2, a <= x, ((1/2)*(a-1)*exp(a-x)+(1/2)*(a+1)*exp(x-a))*_C1+((1/2)*exp(a-x)+(1/2)*exp(x-a))*_C2)

(6)

 

 

The solution is easy to calculate by hand

We just solve the (quite trivial) DE over the intervals x < a and x > 0

separately, and patch the two solutions by requiring the continuity

of u(x) and diff(u(x), x) at x = a.  We get

sol := piecewise(x < a,
        x*c[1] + c[2],
        ((a*c[1] + c[1] + c[2])*exp(x))/(2*exp(a)) + ((a*c[1] - c[1] + c[2])*exp(-x))/(2*exp(-a)));

sol := piecewise(x < a, x*c[1]+c[2], (a*c[1]+c[1]+c[2])*exp(x)/(2*exp(a))+(a*c[1]-c[1]+c[2])*exp(-x)/(2*exp(-a)))

(7)

 

Download badHeavi.mw

I answered this question about 6 hours ago, after which both the question and my answer disappeared.

I feel disinclined to give the same lengthy explanations about the required corrections again, so the attached is posted without comment.


 

  restart;
  with(plots):

  eq1:= diff(f(x), x$3)
        +
        1/2*(1-phi)^2.5*(1-phi+phi*rho__s/rho__f1)*(eta*cos__omega + f(x)*sin__omega)*diff(f(x), x$2)
        +
        (1-phi)^2.5*M*sin(alpha)^2*(1-diff(f(x),x))
        +
        (1-phi)^2.5*(1-phi+phi*rho__beta__s/rho__beta__f1)*lambda__T*theta(x);

  eq2:= K__nf/K__f*diff(theta(x),x$2)
        +
        Pr/2*(eta*cos__omega + f(x)*sin__omega)*diff(theta(x),x);
#
# The OP's original list of boundary conditions contained f(1)=0.
# In a 1-dimensional BVP only two boundaries are allowed, so the
# condition f(1)=0 has been "replaced" by the condition
#
#    D(f)(0) = val
#
# A "shooting" method will be used later to determine a value for
# "val", whihc ensures that the original BC ( ie f(1)=0 ) is
# satisfied
#
  bcs := f(0) = 0, D(f)(0) = val, f(10) = 1, theta(0) = 1, theta(10) = 0;

  params:= [ K__f=0.613, K__nf=0.6842, M=1, Pr=6.2,
             alpha=0, eta=0, phi=0.05, rho__f1=997.1,
             rho__s=5200, cos__omega=1, lambda__T=0,
             rho__beta__f1=20939.1, rho__beta__s=997.1,
             sin__omega=1
           ];
#
# So the ODE system with all parameter values inserted is
#
  odesys:=eval([eq1, eq2], params);

diff(diff(diff(f(x), x), x), x)+(1/2)*(1-phi)^2.5*(1-phi+phi*rho__s/rho__f1)*(eta*cos__omega+f(x)*sin__omega)*(diff(diff(f(x), x), x))+(1-phi)^2.5*M*sin(alpha)^2*(1-(diff(f(x), x)))+(1-phi)^2.5*(1-phi+phi*rho__beta__s/rho__beta__f1)*lambda__T*theta(x)

 

K__nf*(diff(diff(theta(x), x), x))/K__f+(1/2)*Pr*(eta*cos__omega+f(x)*sin__omega)*(diff(theta(x), x))

 

f(0) = 0, (D(f))(0) = val, f(10) = 1, theta(0) = 1, theta(10) = 0

 

[K__f = .613, K__nf = .6842, M = 1, Pr = 6.2, alpha = 0, eta = 0, phi = 0.5e-1, rho__f1 = 997.1, rho__s = 5200, cos__omega = 1, lambda__T = 0, rho__beta__f1 = 20939.1, rho__beta__s = 997.1, sin__omega = 1]

 

[diff(diff(diff(f(x), x), x), x)+.5325197465*f(x)*(diff(diff(f(x), x), x)), 1.116150082*(diff(diff(theta(x), x), x))+3.100000000*f(x)*(diff(theta(x), x))]

(1)

#
# The shooting method
#
# This determines a value for D(f)(0) such that the
# OP's original desired condition f(1)=0 is satisfied
#
  SM:= proc( shoot )
             local ans:
             if type( shoot, numeric)
             then ans:= dsolve
                        ( eval
                          ( [odesys[], bcs],
                            val=shoot
                          ),
                          numeric
                        ):
                  return rhs(ans(1)[2]);
             else return 'procname(_passed)'
             fi;
       end proc:
  sv:= fsolve( SM );

-0.1290531852e-1

(2)

#
# Solve the system
#
  sol:= dsolve
        (  eval
           ( [odesys[], bcs],
             val=sv
           ),
          numeric
        ):
#
# Check that when x=1, f(x)=0, which was OP's desired condition
#
  sol(1)[1..2];
#
# Plot the results
#
  odeplot
  ( sol,
    [ [x, f(x)],
      [x, theta(x)]
    ],
    x = 0 .. 10,
    color=[red, blue],
    legend=[typeset(f(x)), typeset(theta(x))]
  );
  

[x = 1., f(x) = HFloat(1.9274077505456594e-12)]

 

 

 


 

Download odeProb.mw

  1. Your ODEs contain both the dependent variables f(x), theta(x) as well as the simple names f, theta. You can't have both. In the attached I have changed all instances of the latter into the former.
  2. Your ODEs have the dependent variables f(x), theta(x), whereas your boundary conditions refer to functions F() and Theta(). In the attached I have fixed the upperCase/lowerCase discrepancy
  3. Your original supplied boundary conditions (with the case fixed, see 2 above) were f(0) = 0, f(1)=0, f(10) = 1, theta(0) = 1, theta(10) = 0. A 1-dimensional BVP can only have two boundaries: you have three. In the attached I have used a shooting method to replace the condition f(1)=0 with D(f)(0)=val. The shooting method determines an appropriate value for the quantity 'val', so that the value f(1) will be 0
  4. The "naming" conventions you have used are pretty awful. You use indexed variables (eg K[f]) when yoiu should be using inert subscripts (eg K__f). You have the variable names sinw and cosw, which in Maple output "look" like sin(w) and cos(w). At first I thought this might be a typo and that the trigonometric functions might be desired. However your parameter list contains sinw=0 and cosw=0. Since there is no value of 'w' for which both sin(w)=0 and cos(w)=0, I decided that this was just a lousy choice of names. In the attached I changed these to sin__omega and cos__omega, whihc (at least partially) helps to avoid confusion with trigonometric functions
  5. There were various other typos, which are hopefully now fixed in the attached.

With the all the changes I have made it is possible that I have introduced something which was not your intent, so I suggest you check the attached very carefully

By the way, this is a BVP system, which cannot be solved using a Runge-Kutta method. However Maple's default method for BVPs (a finite difference method) works quite well

  restart;
  with(plots):

  eq1:= diff(f(x), x$3)
        +
        1/2*(1-phi)^2.5*(1-phi+phi*rho__s/rho__f1)*(eta*cos__omega + f(x)*sin__omega)*diff(f(x), x$2)
        +
        (1-phi)^2.5*M*sin(alpha)^2*(1-diff(f(x),x))
        +
        (1-phi)^2.5*(1-phi+phi*rho__beta__s/rho__beta__f1)*lambda__T*theta(x);

  eq2:= K__nf/K__f*diff(theta(x),x$2)
        +
        Pr/2*(eta*cos__omega + f(x)*sin__omega)*diff(theta(x),x);
#
# The OP's original list of boundary conditions contained f(1)=0.
# In a 1-dimensional BVP only two boundaries are allowed, so the
# condition f(1)=0 has been "replaced" by the condition
#
#    D(f)(0) = val
#
# A "shooting" method will be used later to determine a value for
# "val", whihc ensures that the original BC ( ie f(1)=0 ) is
# satisfied
#
  bcs := f(0) = 0, D(f)(0) = val, f(10) = 1, theta(0) = 1, theta(10) = 0;

  params:= [ K__f=0.613, K__nf=0.6842, M=1, Pr=6.2,
             alpha=0, eta=0, phi=0.05, rho__f1=997.1,
             rho__s=5200, cos__omega=1, lambda__T=0,
             rho__beta__f1=20939.1, rho__beta__s=997.1,
             sin__omega=1
           ];

diff(diff(diff(f(x), x), x), x)+(1/2)*(1-phi)^2.5*(1-phi+phi*rho__s/rho__f1)*(eta*cos__omega+f(x)*sin__omega)*(diff(diff(f(x), x), x))+(1-phi)^2.5*M*sin(alpha)^2*(1-(diff(f(x), x)))+(1-phi)^2.5*(1-phi+phi*rho__beta__s/rho__beta__f1)*lambda__T*theta(x)

 

K__nf*(diff(diff(theta(x), x), x))/K__f+(1/2)*Pr*(eta*cos__omega+f(x)*sin__omega)*(diff(theta(x), x))

 

f(0) = 0, (D(f))(0) = val, f(10) = 1, theta(0) = 1, theta(10) = 0

 

[K__f = .613, K__nf = .6842, M = 1, Pr = 6.2, alpha = 0, eta = 0, phi = 0.5e-1, rho__f1 = 997.1, rho__s = 5200, cos__omega = 1, lambda__T = 0, rho__beta__f1 = 20939.1, rho__beta__s = 997.1, sin__omega = 1]

(1)

#
# The shooting method
#
# This determines a value for D(f)(0) such that the
# OP's original desired condition f(1)=0 is satisfied
#
  SM:= proc( shoot )
             local ans:
             if type( shoot, numeric)
             then ans:= dsolve
                        ( eval
                          ( eval
                            ( [eq1, eq2, bcs],
                              params
                            ),
                            val=shoot
                          ),
                          numeric
                        ):
                  return rhs(ans(1)[2]);
             else return 'procname(_passed)'
             fi;
       end proc:
  sv:= fsolve( SM );

-0.1290531852e-1

(2)

#
# Solve the system
#
  sol:= dsolve
        (  eval
           ( eval
             ( [eq1, eq2, bcs],
                params
             ),
             val=sv
           ),
          numeric
        ):
#
# Check that when x=1, f(x)=0, which was OP's desired condition
#
  sol(1)[1..2];
#
# Plot the results
#
  odeplot
  ( sol,
    [ [x, f(x)],
      [x, theta(x)]
    ],
    x = 0 .. 10,
    color=[red, blue],
    legend=[typeset(f(x)), typeset(theta(x))]
  );
  

[x = 1., f(x) = HFloat(1.9274077505456594e-12)]

 

 

 

Download odeProb.mw

Try

8*(cos(Pi/2)+I*sin(Pi/2));

If you omit the multiplication sign as in

8(cos(Pi/2)+I*sin(Pi/2));

then you Maple interprets this as a function named '8' - ie 8() to which you can supply any argument. And it doesn't matter what argument you supply to this function, the answer will always be 8!

because from the equations you provide, the only "sensible" conclusion I can draw is shown in the attached.

This probably isn't what you want!

But is correct, based on the information you have provided

restart

AA := [diff(ZETA[1](t), t) = -(1/3)*C[2, 1](t), diff(ZETA[1](t), t) = -(1/5)*C[4, 1](t), diff(ZETA[2](t), t) = -(1/3)*C[2, 2](t), diff(ZETA[2](t), t) = -(1/5)*C[4, 2](t), diff(ZETA[3](t), t) = -(1/3)*C[2, 3](t), diff(ZETA[3](t), t) = -(1/5)*C[4, 3](t), diff(ZETA[4](t), t) = -(1/3)*C[2, 4](t), diff(ZETA[4](t), t) = -(1/5)*C[4, 4](t)]

[diff(ZETA[1](t), t) = -(1/3)*C[2, 1](t), diff(ZETA[1](t), t) = -(1/5)*C[4, 1](t), diff(ZETA[2](t), t) = -(1/3)*C[2, 2](t), diff(ZETA[2](t), t) = -(1/5)*C[4, 2](t), diff(ZETA[3](t), t) = -(1/3)*C[2, 3](t), diff(ZETA[3](t), t) = -(1/5)*C[4, 3](t), diff(ZETA[4](t), t) = -(1/3)*C[2, 4](t), diff(ZETA[4](t), t) = -(1/5)*C[4, 4](t)]

(1)

seq(-rhs(AA[2*j-1]) = -rhs(AA[2*j]), j = 1 .. 4)

(1/3)*C[2, 1](t) = (1/5)*C[4, 1](t), (1/3)*C[2, 2](t) = (1/5)*C[4, 2](t), (1/3)*C[2, 3](t) = (1/5)*C[4, 3](t), (1/3)*C[2, 4](t) = (1/5)*C[4, 4](t)

(2)

 

Download crapSys.mw

 

   - why do you want to extract coordinates from a spacecurve?

If you can supply Maple with enough information to generate a spacecurve, then you can generate x-, y-, z-values for any parameter(s) - so why bother with the spacecurve? Sure, it will give you values, for z, y,  z, for a restricted set of the parameter(s) values which you have, where these parameter(s) values are determined by Maple's adaptive plotting routines - but why not just calculate any vakue if x, y, z. directly. Because iif the spacecurve() command can dio it, then so can you.

Unfortunately you prcvide insufficient infirmation to demonstrate how this might be done. The only things I can surmise form the completely inadequate code which you present is that each of 'x', 'y', 'z' are functions of a single variable. So for some value, say 'alpha' of this variable, why not just compute x(alpha), y(alpha), z(alpha), and forget the spacecurve altogether?

Perhaps if you had provided sufficient code to make your question "executable", at least capable of producing the spacecurve, then I could make this explanation clearer.

Rule No 1: Ask an unclear question and you will get an unclear answer

minor typos, which are fixed in the attached

  restart:
  with(plots):
  with(plottools):
  Vdot := proc (U, V)local i: add(U[i]*V[i], i = 1 .. 2) end proc:
  dist := proc (M, N) sqrt(Vdot(expand(M-N), expand(M-N))) end proc:
  ngon := n -> local i: [seq([cos(2*Pi*i/n), sin(2*Pi*i/n)], i = 1 .. n)]:
  theta := (2*Pi)/5:
  poly := [seq([cos(k*theta), sin(k*theta)], k = 1 .. 5)]:
  Ii := [0, 1/2]:
  H := [-1/4, 0]:
  r := dist(Ii, H):
  theta := (2*Pi)/5:
  p1 := pointplot([seq([cos(k*theta), sin(k*theta)], k = 0 .. 5)], symbol = solidcircle, color = red, symbolsize = 10):
  p2 := textplot([seq([cos(k*theta), sin(k*theta), cat("M", k)], k = 0 .. 4)], align = ["above", "right"]):
  cir1 := circle([0, 0], 1/2, color = green, linestyle=dashdot):
  cir2 := circle([-1/4, 0], r, color = black):
  cir3:=circle([0,0],1,color=red):
  display([p1, p2, cir1, cir2, cir3, polygonplot(poly, thickness = 5, color = blue, transparency = 0.95)], axes = normal);

 

 

Download pentplot.mw

It appears that visualization routines within "Student" packages come with their own set of plot options, whch are only a subset of those available for "normal" plot() and plot3d() commands. You can see the available options using ?Student Plot Options.

To my amazement, no "color" option is available!!!. So in the OP's case, in the option,

volumeoptions = [color = blue, transparency = 0.6]

The color sub-option is simply ignored !

It seems that the visualization routines within student packages come with a default palette - so the first object in a plot will always use the first color in the palette, second object will be the second palette color, and so on. By default, the color palette is "Niagara" which you can view here ?Niagara Color Palette.

Thus the only way to change colors is to add desired colors to the beginning of the default palette, using the Student:-SetColors() command, whihch I have done in the attached to add blue, red green. Note that in the resulting plot, the first object (ie the volume) is "blue" and the second object (ie the generating line) is red.

  restart:
  Student:-SetColors(blue, red, green);
  with( Student:-Calculus1):
  VolumeOfRevolution( 4,
                      x = 1 .. 2,
                      volumeoptions = [transparency = 0.6],
                      orientation = [270, 0, 15],
                      view = [0 .. 3, -5 .. 5, -5 .. 5],
                      labels = [x, y, z],
                      output = plot,
                      axis = horizontal,
                      scaling = constrained
                    );

[blue, red, green, "#3E578A", "#780072", "#00786A", "#604191", "#004A78", "#784C00", "#91414A", "#3E738A", "#78003B", "#00783F", "#914186", "#510078", "#777800"]

 

 

 

Download addColStud.mw

 

They are two entirely different concepts.

If you need a "toy" example to illustrate the difference, consider sin(x)/x. This has a limiting value of 1 as x->0. Hoever if you substitute x=0, you get 0/0 - which is what, exactly?

This site really isn't the best place to learn high-school mathematics

you state

Here psi is a general wave function from schrodinger wave equation.

In which case it probably ought to be Psi(x,t) - but I wouldn't use that name, because Psi() is one of Maple's built-in functions and Psi(x,t) will be interpreted as  the x-th derivative of the digamma function Psi(t). Just avoid the problem by using Phi(x,t) instead,

In the attached I have unapply() to evaluate the arguments of all necessary functions as far as possible.

One still doesn't get too far, because there are still many unknown functions in the final integrand eg Phi(x,t), mu(t), and x(t) - so no integration can actually be performed.

Another piece of advice I wouldn't use a functon 'x(t)' and a scalar independent variable named 'x' in the same worksheet - this is just asking for "subtle" problems.

Anyhow, for what it is worth, you may(?) find the attached helpful

  restart:

  f := unapply
       ( abs(Phi(x,t))^2,
         [x,t]
       );

proc (x, t) options operator, arrow; abs(Phi(x, t))^2 end proc

(1)

  a := unapply
       ( piecewise
         ( 0 <= t and t <= 1,
           1.5*t,
           1 <= t and t <= 2,
           1.5*(2 - t)
         ),
         t
       );

a := proc (t) options operator, arrow; piecewise(0 <= t and t <= 1, 1.5*t, 1 <= t and t <= 2, 3.0+(-1)*1.5*t) end proc

(2)

  y[a] := unapply
          ( piecewise
            ( 0 <= t and t <= 0.1,
              a(t),
              0.1 <= t and t <= 0.2,
              -a(t)
            ),
            t
          );

y[a] := proc (t) options operator, arrow; piecewise(0 <= t and t <= .1, piecewise(0 <= t and t <= 1, 1.5*t, 1 <= t and t <= 2, 3.0+(-1)*1.5*t), .1 <= t and t <= .2, -piecewise(0 <= t and t <= 1, 1.5*t, 1 <= t and t <= 2, 3.0+(-1)*1.5*t)) end proc

(3)

  y := unapply
       ( y[a](t) + mu(t),
         t
       );

y := proc (t) options operator, arrow; piecewise(0 <= t and t <= .1, piecewise(0 <= t and t <= 1, 1.5*t, 1 <= t and t <= 2, 3.0+(-1)*1.5*t), .1 <= t and t <= .2, -piecewise(0 <= t and t <= 1, 1.5*t, 1 <= t and t <= 2, 3.0+(-1)*1.5*t))+mu(t) end proc

(4)

  w := unapply
       ( int
         ( x(t)*f(x, t),
           x
         ),
         t
       );

proc (t) options operator, arrow; int(x(t)*abs(Phi(x, t))^2, x) end proc

(5)

  v := unapply
       ( y(t) - w(t)*w(t),
         t
       );

v := proc (t) options operator, arrow; piecewise(0 <= t and t <= .1, piecewise(0 <= t and t <= 1, 1.5*t, 1 <= t and t <= 2, 3.0+(-1)*1.5*t), .1 <= t and t <= .2, -piecewise(0 <= t and t <= 1, 1.5*t, 1 <= t and t <= 2, 3.0+(-1)*1.5*t))+mu(t)-(int(x(t)*abs(Phi(x, t))^2, x))^2 end proc

(6)

  eqn:= diff(K(x, t), t) = beta*v(t)*f(x, t);

diff(K(x, t), t) = beta*(piecewise(0 <= t and t <= .1, piecewise(0 <= t and t <= 1, 1.5*t, 1 <= t and t <= 2, 3.0-1.5*t), .1 <= t and t <= .2, -piecewise(0 <= t and t <= 1, 1.5*t, 1 <= t and t <= 2, 3.0-1.5*t))+mu(t)-(int(x(t)*abs(Phi(x, t))^2, x))^2)*abs(Phi(x, t))^2

(7)

  sol:= map( int, eqn, t);

K(x, t) = int(beta*(piecewise(0 <= t and t <= .1, piecewise(0 <= t and t <= 1, 1.5*t, 1 <= t and t <= 2, 3.0-1.5*t), .1 <= t and t <= .2, -piecewise(0 <= t and t <= 1, 1.5*t, 1 <= t and t <= 2, 3.0-1.5*t))+mu(t)-(int(x(t)*abs(Phi(x, t))^2, x))^2)*abs(Phi(x, t))^2, t)

(8)

#
# Expand the integral on the rhs of the above
#

  lhs(sol)=IntegrationTools:-Expand(rhs(sol));

K(x, t) = beta*(int(abs(Phi(x, t))^2*piecewise(0 <= t and t <= .1, piecewise(0 <= t and t <= 1, 1.5*t, 1 <= t and t <= 2, 3.0-1.5*t), .1 <= t and t <= .2, -piecewise(0 <= t and t <= 1, 1.5*t, 1 <= t and t <= 2, 3.0-1.5*t)), t))+beta*(int(abs(Phi(x, t))^2*mu(t), t))-beta*(int(abs(Phi(x, t))^2*(int(x(t)*abs(Phi(x, t))^2, x))^2, t))

(9)

 

Download oddint.mw

 

I think this might depend (a lot?) on how "generally applicable" you want the process to be. For the example you give,the simple code in the attached will work, For other (possibky similar, but slightly different?) problems, some "tuning" might be necessary, but I wouldn't expect such "tuning" to be difficult

  with(numapprox):
  op~(1, [op(chebyshev(exp(x),x))]);

[HFloat(1.2660658777520082), HFloat(1.1303182079849698), HFloat(0.2714953395340765), HFloat(0.044336849848663804), HFloat(0.005474240442093705), HFloat(5.429263119139931e-4), HFloat(4.497732295427603e-5), HFloat(3.1984364624457973e-6), HFloat(1.992124806415823e-7), HFloat(1.103677170949997e-8), HFloat(5.505896979790788e-10)]

(1)

 

Download extrCoeff.mw

produces correct results! You can see this by reconstructing the original equations by using the matrix and vector of right-hand-sides produced by the GenerateMatrix() command to reconstruct the original equations. This is shown in the final execution group of the attached.


(Normally one would do this "reconstruction" using the GenerateEquations() command but this doesn't seems to like the fact that your designated "variables" are not simple names.)
 

restart

N := 2; M := 2

a := 1b := 1

Qa := [-0.5379667864e-1*(diff(tau[1, 1](t), t, t))+7.862351349*10^(-11)*tau[2, 1](t)-8.050993899*10^(-12)*(diff(tau[2, 1](t), t, t))+.1166068042*(diff(tau[1, 2](t), t))+2.181309895*10^(-11)*(diff(tau[2, 2](t), t))+.5309519363*tau[1, 1](t) = 0, -1.265965258*10^(-11)*(diff(tau[1, 1](t), t, t))+.4884414390*tau[2, 1](t)-0.4948946475e-1*(diff(tau[2, 1](t), t, t))+2.738892495*10^(-11)*(diff(tau[1, 2](t), t))+.1340883970*(diff(tau[2, 2](t), t))+1.246469610*10^(-10)*tau[1, 1](t) = 0, 3.649366137*10^(-10)*tau[2, 2](t)-9.135908950*10^(-12)*(diff(tau[2, 2](t), t, t))-5.160677740*10^(-11)*(diff(tau[2, 1](t), t))+1.953765755*tau[1, 2](t)-0.4948946473e-1*(diff(tau[1, 2](t), t, t))-.3476543209*(diff(tau[1, 1](t), t)) = 0, 2.246672656*tau[2, 2](t)-0.5690888318e-1*(diff(tau[2, 2](t), t, t))-.3198194887*(diff(tau[2, 1](t), t))+4.602903411*10^(-10)*tau[1, 2](t)-1.159417294*10^(-11)*(diff(tau[1, 2](t), t, t))-8.175817372*10^(-11)*(diff(tau[1, 1](t), t)) = 0]

Q1 := [seq(seq(diff(tau[i, j](t), t), i = 1 .. M), j = 1 .. N)]

with(LinearAlgebra)

C, R := GenerateMatrix(simplify(Qa), Q1); `~`[`=`](`~`[`-`](convert(C.Matrix(4, 1, Q1), list), convert(R, list)), 0); is(% = Qa)

[-0.5379667864e-1*(diff(diff(tau[1, 1](t), t), t))+0.7862351349e-10*tau[2, 1](t)-0.8050993899e-11*(diff(diff(tau[2, 1](t), t), t))+.1166068042*(diff(tau[1, 2](t), t))+0.2181309895e-10*(diff(tau[2, 2](t), t))+.5309519363*tau[1, 1](t) = 0, -0.1265965258e-10*(diff(diff(tau[1, 1](t), t), t))+.4884414390*tau[2, 1](t)-0.4948946475e-1*(diff(diff(tau[2, 1](t), t), t))+0.2738892495e-10*(diff(tau[1, 2](t), t))+.1340883970*(diff(tau[2, 2](t), t))+0.1246469610e-9*tau[1, 1](t) = 0, 0.3649366137e-9*tau[2, 2](t)-0.9135908950e-11*(diff(diff(tau[2, 2](t), t), t))-0.5160677740e-10*(diff(tau[2, 1](t), t))+1.953765755*tau[1, 2](t)-0.4948946473e-1*(diff(diff(tau[1, 2](t), t), t))-.3476543209*(diff(tau[1, 1](t), t)) = 0, 2.246672656*tau[2, 2](t)-0.5690888318e-1*(diff(diff(tau[2, 2](t), t), t))-.3198194887*(diff(tau[2, 1](t), t))+0.4602903411e-9*tau[1, 2](t)-0.1159417294e-10*(diff(diff(tau[1, 2](t), t), t))-0.8175817372e-10*(diff(tau[1, 1](t), t)) = 0]

 

true

(1)

 


 

Download genMat1.mw

as in the attached

  restart;
  with(plots):
  P:= [.6286420119, -.6286420119, 0., 0., 0., 0., 0., 0., 0., 0., 0.]:
  Q:= [2.106333379, 2.106333379, 4.654463885, 7.843624703, 10.99193295, 14.13546782, 17.27782732, 20.41978346, 23.56157073, 26.70327712, 29.84494078]:
  W:= zip((x,y)->[x,y], P, Q);
  pointplot( W,
             axes=boxed,
             view=[-1..1, 0..30],
             symbol=solidcircle,
             symbolsize=16,
             color=red);
  display( seq(pointplot(W[j]), j = 1 .. numelems(W)),
           insequence = true,
           axes=boxed,
           view=[-1..1, 0..30],
           symbol=solidcircle,
           symbolsize=16,
           color=red
         );
  display( seq(pointplot(W[1..j]), j = 1 .. numelems(W)),
           insequence = true,
           axes=boxed,
           view=[-1..1, 0..30],
           symbol=solidcircle,
           symbolsize=16,
           color=red
         );

[[.6286420119, 2.106333379], [-.6286420119, 2.106333379], [0., 4.654463885], [0., 7.843624703], [0., 10.99193295], [0., 14.13546782], [0., 17.27782732], [0., 20.41978346], [0., 23.56157073], [0., 26.70327712], [0., 29.84494078]]

 

 

 

 

 

 


 

Download anims.mw

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