Preben Alsholm

11754 Reputation

22 Badges

15 years, 305 days

MaplePrimes Activity


These are replies submitted by Preben Alsholm

@vv Your example doesn't really suggest that does it? The values at t = 0 for U and X are certainly different:

 

restart;

Digits:=30:
  

ode := X(t)*diff(X(t), t, t) - diff(X(t), t)/(1 + diff(X(t), t)^2) - (100000000000000*t^14 + 7000000000000*t^12 + 110000000000*t^10 - 500000000*t^8 - 43000000*t^6 - 170000*t^4 - 1700*t^2 - 1)/(2*(100*t^2 + 1)^4*(50000000*t^8 + 2000000*t^6 + 35000*t^4 + 100*t^2 + 1));
          

X(t)*(diff(diff(X(t), t), t))-(diff(X(t), t))/(1+(diff(X(t), t))^2)-(1/2)*(100000000000000*t^14+7000000000000*t^12+110000000000*t^10-500000000*t^8-43000000*t^6-170000*t^4-1700*t^2-1)/((100*t^2+1)^4*(50000000*t^8+2000000*t^6+35000*t^4+100*t^2+1))

U := t -> t/((t*10)^2+1):
          

simplify(eval(ode, X=U)), [U(0), D(U)(0)];
 

0, [0, 1]

SOL:=dsolve([ode, X(1/2)=0.0211219739941351352807211288991, D(X)(1/2)=0.0540921883052830726848992435887], numeric,abserr=1e-15,relerr=1e-13);
          

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 := 30; 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 .. 26, [( 1 ) = (datatype = sfloat, order = C_order, storage = rectangular), ( 2 ) = (datatype = sfloat, order = C_order, storage = rectangular), ( 3 ) = ([0, 0, 0, Array(1..0, 1..2, {}, order = C_order)]), ( 4 ) = (Array(1..63, {(1) = 2, (2) = 2, (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) = 1, (22) = 1, (23) = 4, (24) = 0, (25) = 2, (26) = 30, (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}, datatype = integer[8])), ( 5 ) = (Array(1..28, {(1) = .500000000000000000000000000000, (2) = 0.1e-12, (3) = 0., (4) = 0.500001e-29, (5) = .500000000000000000000000000000, (6) = 0.296338439495637901017502167099e-4, (7) = 0., (8) = 0.1e-12, (9) = 0., (10) = 0., (11) = 0., (12) = 0., (13) = 1., (14) = 0., (15) = .49999999999999, (16) = 0., (17) = 1., (18) = 1., (19) = 0., (20) = 0., (21) = 1., (22) = 1., (23) = 0., (24) = 0., (25) = 0.1e-14, (26) = 0., (27) = 0., (28) = 0.}, order = C_order)), ( 6 ) = (Array(1..2, {(1) = 0.211219739941351352807211288991e-1, (2) = 0.540921883052830726848992435887e-1}, order = C_order)), ( 7 ) = ([Array(1..4, 1..7, {(1, 1) = 0., (1, 2) = 26., (1, 3) = 39., (1, 4) = 96., (1, 5) = 104., (1, 6) = 52., (1, 7) = 104., (2, 1) = 33440., (2, 2) = 0., (2, 3) = 146432., (2, 4) = 142805., (2, 5) = -50787., (2, 6) = 10260., (2, 7) = 282150., (3, 1) = 1045., (3, 2) = 0., (3, 3) = -11264., (3, 4) = -10985., (3, 5) = 7524., (3, 6) = 13680., (3, 7) = 376200., (4, 1) = 1629155., (4, 2) = 0., (4, 3) = 6769664., (4, 4) = 340535., (4, 5) = -101574., (4, 6) = -800280., (4, 7) = 13062500.}, 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., (2, 1) = 1., (2, 2) = 0., (2, 3) = 0., (2, 4) = 0., (2, 5) = 0., (2, 6) = 4., (3, 1) = 3., (3, 2) = 9., (3, 3) = 0., (3, 4) = 0., (3, 5) = 0., (3, 6) = 32., (4, 1) = 1932., (4, 2) = -7200., (4, 3) = 7296., (4, 4) = 0., (4, 5) = 0., (4, 6) = 2197., (5, 1) = 8341., (5, 2) = -32832., (5, 3) = 29440., (5, 4) = -845., (5, 5) = 0., (5, 6) = 4104., (6, 1) = -6080., (6, 2) = 41040., (6, 3) = -28352., (6, 4) = 9295., (6, 5) = -5643., (6, 6) = 20520.}, order = C_order), Array(1..6, {(1) = 0., (2) = .386, (3) = .210, (4) = .630, (5) = 1., (6) = 1.}, order = C_order), Array(1..6, {(1) = .25, (2) = -.1043, (3) = .1035, (4) = -0.362e-1, (5) = 0., (6) = 0.}, 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) = 1.54400000000000000000000000000, (2, 2) = 0., (2, 3) = 0., (2, 4) = 0., (2, 5) = 0., (3, 1) = .946678528081553286149092671142, (3, 2) = .255701169898258116368870256812, (3, 3) = 0., (3, 4) = 0., (3, 5) = 0., (4, 1) = 3.31482518706848855878639615336, (4, 2) = 2.89612401597212315251490972823, (4, 3) = .998641913997780725707304795298, (4, 4) = 0., (4, 5) = 0., (5, 1) = 1.22122450922627482364750744120, (5, 2) = 6.01913448128775290549318365614, (5, 3) = 12.5370833293208745721773449832, (5, 4) = -.687886036105895135654889206414, (5, 5) = 0., (6, 1) = 1.22122450922627482364750744120, (6, 2) = 6.01913448128775290549318365614, (6, 3) = 12.5370833293208745721773449832, (6, 4) = -.687886036105895135654889206414, (6, 5) = 1.}, 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) = -5.66880000000000000000000000000, (2, 2) = 0., (2, 3) = 0., (2, 4) = 0., (2, 5) = 0., (3, 1) = -2.43009335683375818512768794859, (3, 2) = -.206359915708912236643547336023, (3, 3) = 0., (3, 4) = 0., (3, 5) = 0., (4, 1) = -.107352905814526218453871436335, (4, 2) = -9.59456225102189431954327672200, (4, 3) = -20.4702861480961548107719410920, (4, 4) = 0., (4, 5) = 0., (5, 1) = 7.49644331396861502581028867134, (5, 2) = -10.2468043146412183182800627326, (5, 3) = -33.9999035281990634994054417818, (5, 4) = 11.7089089320615954381414222772, (5, 5) = 0., (6, 1) = 8.08324679592241092908495062968, (6, 2) = -7.98113298806278547829882004219, (6, 3) = -31.5215943287437290544342145785, (6, 4) = 16.3193054312313618929244027333, (6, 5) = -6.05881823883405376327046553946}, 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) = 10.1262350834469120570913462177, (2, 2) = -7.48799587760763313332363461989, (2, 3) = -34.8009186155574113979166343882, (2, 4) = -7.99277170756872733717900590859, (2, 5) = 1.02513772329562064439580564715, (3, 1) = -.676280339280689777028659735967, (3, 2) = 6.08771465167860644619433469196, (3, 3) = 16.4308432089246306468843834297, (3, 4) = 24.7672251141836512529640785251, (3, 5) = -6.59438912571678161124446044889}, order = C_order)]), ( 9 ) = ([Array(1..2, {(1) = 0.100000000000000000000000000000e-1, (2) = 0.100000000000000000000000000000e-1}, order = C_order), Array(1..2, {(1) = 0., (2) = 0.}, order = C_order), Array(1..2, {(1) = 0., (2) = 0.}, order = C_order), Array(1..2, {(1) = 0., (2) = 0.}, order = C_order), Array(1..2, {(1) = 0., (2) = 0.}, order = C_order), Array(1..2, 1..2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0.}, order = C_order), Array(1..2, 1..2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0.}, order = C_order), Array(1..2, {(1) = 0., (2) = 0.}, order = C_order), Array(1..2, 1..2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0.}, order = C_order), Array(1..2, 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.}, order = C_order), Array(1..2, {(1) = 0, (2) = 0}, datatype = integer[8]), Array(1..2, {(1) = 0., (2) = 0.}, order = C_order), Array(1..2, {(1) = 0., (2) = 0.}, order = C_order), Array(1..2, {(1) = 0., (2) = 0.}, order = C_order), Array(1..2, {(1) = 0., (2) = 0.}, order = C_order), Array(1..2, {(1) = 0., (2) = 0.}, order = C_order), Array(1..4, {(1) = 0., (2) = 0., (3) = 0., (4) = 0.}, order = C_order), Array(1..2, {(1) = 0, (2) = 0}, datatype = integer[8])]), ( 8 ) = ([Array(1..2, {(1) = 0.211219739941351352807211288991e-1, (2) = 0.540921883052830726848992435887e-1}, order = C_order), Array(1..2, {(1) = 0., (2) = 0.}, order = C_order), Array(1..2, {(1) = 0.540921883052830726848992435887e-1, (2) = 4.34617387994087335834553944785}, order = C_order), 0, 0]), ( 11 ) = (Array(1..6, 0..2, {(1, 1) = 0., (1, 2) = 0., (2, 0) = 0., (2, 1) = 0., (2, 2) = 0., (3, 0) = 0., (3, 1) = 0., (3, 2) = 0., (4, 0) = 0., (4, 1) = 0., (4, 2) = 0., (5, 0) = 0., (5, 1) = 0., (5, 2) = 0., (6, 0) = 0., (6, 1) = 0., (6, 2) = 0.}, order = C_order)), ( 10 ) = ([proc (N, X, Y, YP) option `[Y[1] = X(t), Y[2] = diff(X(t),t)]`; YP[2] := -(-Y[2]/(Y[2]^2+1)-(1/2)*(100000000000000*X^14+7000000000000*X^12+110000000000*X^10-500000000*X^8-43000000*X^6-170000*X^4-1700*X^2-1)/((100*X^2+1)^4*(50000000*X^8+2000000*X^6+35000*X^4+100*X^2+1)))/Y[1]; YP[1] := Y[2]; 0 end proc, -1, 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] = X(t), Y[2] = diff(X(t),t)]`; YP[2] := -(-Y[2]/(Y[2]^2+1)-(1/2)*(100000000000000*X^14+7000000000000*X^12+110000000000*X^10-500000000*X^8-43000000*X^6-170000*X^4-1700*X^2-1)/((100*X^2+1)^4*(50000000*X^8+2000000*X^6+35000*X^4+100*X^2+1)))/Y[1]; YP[1] := Y[2]; 0 end proc, -1, 0, 0, 0, 0, 0, 0, 0, 0]), ( 22 ) = (0), ( 23 ) = (0), ( 20 ) = ([]), ( 21 ) = (0), ( 26 ) = (Array(1..0, {})), ( 25 ) = (Array(1..0, {})), ( 24 ) = (0)  ] ))  ] ); _y0 := Array(0..2, {(1) = .500000000000000000000000000000, (2) = 0.211219739941351352807211288991e-1}); _vmap := array( 1 .. 2, [( 1 ) = (1), ( 2 ) = (2)  ] ); _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 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, X(t), diff(X(t), 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

SOL(0);


 

[t = 0., X(t) = -0.1135354542745714989743413776e-7, diff(X(t), t) = 1.00000024659796551712607712249]

plots:-odeplot(SOL, [t,X(t)-U(t)],0..0.2);

plots:-odeplot(SOL, [t,log10(abs(X(t)-U(t)))],0..0.5);

 


 

Download MaplePrimes20-08-15_ode_problem.mwMaplePrimes20-08-15_ode_problem.mw

@mmcdara I believe that your ode is unstable in the forward direction, i.e. as t -> infinity, but stable in the opposite direction.
If I'm right and you are interested in a solution on the finite interval t = 0..t0, then start the solution at t0.
Since you only know X and D(X) at 0 you could try use a shooting method.
But even if you succeed in find starting values (faking not knowing U) for a solution starting at t = t0 (t0 > 0), then that solution will only be good on t = 0..t0. Just try using X(t0) = U(t0) and D(X)(t0) = D(U)(t0) as your initial contions.
You get perfect results for t = 0..t0, but for t > t0 not so.
An example:
Here I chose t0 = 1 and plottet X(t) on 0..1.35:

@pik1432 It is easy to write down several ode systems all with equilibria coming from solving your algebraic equations.
Just multiply say 3 of these equations by minus 1 and the equilbria are the same, but the jacobian and its eigenvalues are not.
Thus stability here must refer to the solving method and obviously must refer to a numerical method as used by fsolve, not an exact as used by solve.
##################################################################################
A trivial one dimensional example is
diff(x(t),t) = x(t) which has jacobian 1 at the equilibrium x = 0 and eigenvalue 1: 0 is unstable.
diff(x(t),t) = -x(t) which has jacobian -1 at the equilibrium x = 0 and eigenvalue -1: 0 is stable.
Yet in both cases determining the equilibrium consists in solving the same basic equation x=0.
 

@pik1432 I forgot that I used expand on your f9n10 as I see that also acer does.

Apparently you are using some hidden code. That doesn't exactly help.

Are you using 2D input?
If so then don't.
Go to Tools/Options/Display/Input display.  Pick Maple Notation (i.e 1D).
Then still with the Options window open go to Interface/Default format for new worksheets. Pick Worksheet.
Now press the button Apply Globally.

Open a new worksheet. I hope you like it better. I do!

If you use solve instead you will get a solution.

You didn't succeed in attaching a file. Use the fat green arrow in the editor.

Use PDEtools:-dchange.

For further help upload a worksheet with your actual system.

You say that you tried to attach the worksheet. It didn't work.

Use the big green arrow in the editor for that purpose.

I opened your worksheet in Maple 12. Ran it. Removed the output. Copied all the input and pasted it into Maple 2020.
Ran it then without any problem:
Basically I never save worksheets with output.

@Suley83 I must disappoint you there. I know nothing about stochastic differential equations.

@Suley83 I made a few comments in your worksheet. They are related to the effect of copying from 2D to 1D.
The comments are made in text lines. You get a text line by going to a new input line (insert one above by using Ctrl+k and below by Ctrl+j) and the do Ctrl+t.
So you can make comments in that way, but also by using # in an input line.

SCI_1D_math_with_comments.mw

@Suley83 When you copy code like mine and paste it into a worksheet be sure to separate regions where necessary or convenient. Use F3.
I strongly advise you to use 1D math input and worksheet mode. I myself hate 2D-math input.

To change go to Tools/Options/Display/Input Display choose Maple Notation.
Then in the same window go to Interface/Default format for new worksheets. Choose Worksheet.

Finally Press Apply Globally.
New worksheets will now be using Maple Notation (1D).
Here is a minimally revised version of your worksheet:
MaplePrimes20-07-30_SCI_help_Progresses.mw

@Suley83 It is no problem to mimic in Maple what is done in the pdf-file.
So I shall restrict myself to that:
 

RHS; # The right hand sides of odeSys
s1,c1:=selectremove(has,RHS[2],S); # For convenience
### I use the notation in the pdf-file, but will not abuse notation and use F and V in two ways.
### Thus the use of JF and JV:
F:= < s1,0 >;
V:= < eval(c1,z=0), eval(RHS[3],z=0) >;
JF1:=VectorCalculus:-Jacobian(F, [C,Iota]);
JV:=  VectorCalculus:-Jacobian(V, [C,Iota]);
###Assuming that a "disease free equilibrium"  has S = N, C = 0, I = 0  we get for RHS: 
eval(RHS,{S=N,C=0,Iota=0});
###These will all be zero if P1 = P2 = 0 and z = N*v. 
###Under those assumptions we get:
JF:=eval(JF1,S=N);
JF.(-JV)^(-1);
###The eigenvalues for this upper triangular matrix are the values in the diagonal, but will 
### (of course) also be found by: 
LinearAlgebra:-Eigenvalues(%);
R0:=max(%) assuming positive;

Assuming then that z, v, and N are connected through z = N*v we get that
Total(t) = S(t) + C(t) + I(t) is constant if N is interpreted as S(0) + C(0) + I(0).

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