Markiyan Hirnyk

Markiyan Hirnyk
8 years, 149 days


These are answers submitted by Markiyan Hirnyk

By OrthogonalExpansions

11 hours ago Markiyan Hirnyk 5673
1 0

How about this?

with(OrthogonalExpansions):
FourierSeries(ln(cos(x)), x = -(1/2)*Pi .. (1/2)*Pi, 14, 'Coefficients');

Because Maple does not find the integral

int(ln(cos(x))*cos(2*i*x), x = -(1/2)*Pi .. (1/2)*Pi) assuming i::posint  ,

the number 14 cannot be replaced by infinity (but it can be replaced by 1400 e. g.). One can easily deduce the general formula.

 

By textplot3d

April 10 2014 Markiyan Hirnyk 5673
1 0

This can be done by the textplot3d command.

with(plots): with(plottools):
textplot3d([1, 2, 3, u[i, j]^k], axes = frame);

 

By workaround

April 09 2014 Markiyan Hirnyk 5673
1 1

It is known that the geometry and geom3d packages have problems with creating indexed objects. However, this can be done as follows.


with(geom3d):``

for i to 2 do for j to 3 do for k to 2 do P[i, j, k] := point(A || s, (1/5)*i, (1/5)*j, (1/5)*k); s := s+1 end do end do end do:

P

RTABLE(18446744074186285054, anything, Array, rectangular, Fortran_order, [], 3, 1 .. 2, 1 .. 3, 1 .. 2)

(1)

 

 

draw(P, symbolsize = 30, axes = frame, view = [0 .. .8, 0 .. .8, 0 .. .8])

 

``

``

If you want  two subscripts and one superscript, then (-1,-1,1) tensor should be created instead of Array.

But I find it to be art for the art's sake because the points in R^3 are not coordinates of any tensor of type (-1,-1,1) by their nature.

Download indexed_points.mw

 

Reference

April 08 2014 Markiyan Hirnyk 5673
2 0

Look at http://www.mapleprimes.com/questions/120636-Give-Me-The-Index-In-A-List-or-Vector .

This link can be found by the "index" search in MaplePrimes at the top of this page.

Case b=0

April 08 2014 Markiyan Hirnyk 5673
0 1

A simple general solution is obtained in the case b=0:

restart; sys := {diff(A(x, t), t) = exp(-2*x*b)*(Y(x, t)-A(x, t)), diff(Y(x, t), `$`(x, 2)) = exp(-2*x*b)*(A(x, t)-Y(x, t))};
ibc := {A(x, 0) = 0, Y(0, t) = .1, (D[1](Y))(0, t) = 0};
sol := pdsolve(eval(sys, b = 0));

PS.

pdetest(sol,eval( sys),b=0);

{0}

 

 

 

 

Download case_b=0.mw

Corrected code

April 03 2014 Markiyan Hirnyk 5673
2 8

Here is the corrected code which works. The plot looks like a straight line.


restart; with(plots); E := .2; phi := .2; alpha := .1; k := 1; lambda := .1; a0 := .5; m := .1; tau := .1; q := Q-1

h3 := 1+lambda*m*x/a0+4*phi*(sum((-1)^(n+1)*cos(2*Pi*(2*n-1)*x)/(2*n-1), n = 1 .. infinity))/Pi:

f := sin(alpha)/E;

proc (x, Q) options operator, arrow; .4991670832-3.527336860*(Q-1)/(1+0.2000000000e-1*x-(.2000000000*I)*(ln((exp((2*I)*Pi*x)+I)/(exp((2*I)*Pi*x)-I))+ln(-(exp((2*I)*Pi*x)-I)/(exp((2*I)*Pi*x)+I)))/Pi)^3 end proc

(1)

DP3 := proc (Q) options operator, arrow; int(evalc(Re(g(x, Q))), x = 0 .. 1, numeric) end proc:
plot(DP3, 0 .. 1, axes = box, linestyle = 1, color = [red], numpoints = 30)

 

DP4 := proc (Q) options operator, arrow; int(evalc(Im(g(x, Q))), x = 0 .. 1, numeric) end proc:
plot(DP4, 0 .. 1, axes = box, linestyle = 1, color = [red], numpoints = 30)

 

``

 

 

``


Download corrected_code.mw

Googling

April 02 2014 Markiyan Hirnyk 5673
0 0

Here are the results of googling "Schwarzschild metric with Maple ".

Workaround

April 01 2014 Markiyan Hirnyk 5673
0 0

plot(eval(int(1/sqrt(a*x^3+1), x), [x = X, a = 1/10])-(eval(int(1/sqrt(a*x^3+1), x), [x = 0, a = 1/10])), X = 0 .. 1);

By DirectSearch:-DataFit

March 30 2014 Markiyan Hirnyk 5673
0 4

Here is an example for your code. This is done as follows.

1, A matrix of the coordinates of the plot points is formed  by getdata command .

2. The equation of the form A*cos(omega1*x+phi1)*sin(omega2*x) is fitted to correspond these coordinates by the FitData command of the DirectSearch package.

 

NULL

restart; with(plots)

EQ1 := -1.233974359*10^7*Pi^2*q2(t)+4.935897435*10^7*q1(t)*Pi^3+.37221250*(diff(q1(t), t, t))*Pi = 0

-12339743.59*Pi^2*q2(t)+49358974.35*q1(t)*Pi^3+.37221250*(diff(diff(q1(t), t), t))*Pi = 0

(1)

EQ2 := -3.084935897*10^6*q2(t)*Pi+1.233974359*10^7*Pi^2*q1(t)+.1623416667*Pi^2*q4(t)-.1623416667*Pi^2*q5(t)-62.11333333*q2(t)*Pi^3-1.501257083*10^(-7)*(diff(q2(t), t, t))*Pi = 0

-3084935.897*q2(t)*Pi+12339743.59*Pi^2*q1(t)+.1623416667*Pi^2*q4(t)-.1623416667*Pi^2*q5(t)-62.11333333*q2(t)*Pi^3-0.1501257083e-6*(diff(diff(q2(t), t), t))*Pi = 0

(2)

EQ3 := 1.540*10^8*q3(t)*Pi^3+442.7500000*Pi^2*q4(t)+442.7500000*Pi^2*q5(t)+.37221250*(diff(q3(t), t, t))*Pi = 0

154000000.0*q3(t)*Pi^3+442.7500000*Pi^2*q4(t)+442.7500000*Pi^2*q5(t)+.37221250*(diff(diff(q3(t), t), t))*Pi = 0

(3)

EQ4 := -.2244000000*q4(t)*Pi^3-.2244000000*q5(t)*Pi^3-168.0539438*(diff(q4(t), t))*Pi-168.0539438*(diff(q5(t), t))*Pi+2.59451500*10^5*Pi^2*(diff(q3(t), t)) = 0

-.2244000000*q4(t)*Pi^3-.2244000000*q5(t)*Pi^3-168.0539438*(diff(q4(t), t))*Pi-168.0539438*(diff(q5(t), t))*Pi+259451.5000*Pi^2*(diff(q3(t), t)) = 0

(4)

EQ5 := -0.8228000000e-4*q4(t)*Pi^3+0.8228000000e-4*q5(t)*Pi^3-0.6161977938e-1*(diff(q4(t), t))*Pi+0.6161977938e-1*(diff(q5(t), t))*Pi-.1046454383*Pi^2*(diff(q2(t), t)) = 0

-0.8228000000e-4*q4(t)*Pi^3+0.8228000000e-4*q5(t)*Pi^3-0.6161977938e-1*(diff(q4(t), t))*Pi+0.6161977938e-1*(diff(q5(t), t))*Pi-.1046454383*Pi^2*(diff(q2(t), t)) = 0

(5)

res := dsolve(`union`(eval({EQ1, EQ2, EQ3, EQ4, EQ5}), {q1(0) = 0.1e-2, q2(0) = 0, q3(0) = 0, q4(0) = 0, q5(0) = 0, (D(q1))(0) = 0, (D(q2))(0) = 0, (D(q3))(0) = 0}), numeric, maxfun = 10^9);

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 .. 20, [( 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)]), ( 5 ) = (Array(1..28, {(1) = .0, (2) = 0.10e-5, (3) = .0, (4) = 0.500001e-14, (5) = .0, (6) = 0.19547402168511487e-13, (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)), ( 4 ) = (Array(1..53, {(1) = 8, (2) = 8, (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) = 1000000000, (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}, datatype = integer[4])), ( 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)]), ( 6 ) = (Array(1..8, {(1) = 0.10e-2, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0}, datatype = float[8], order = C_order)), ( 10 ) = ([proc (N, X, Y, YP) option `[Y[1] = q1(t), Y[2] = diff(q1(t),t), Y[3] = q2(t), Y[4] = diff(q2(t),t), Y[5] = q3(t), Y[6] = diff(q3(t),t), Y[7] = q4(t), Y[8] = q5(t)]`; YP[2] := 104151386.128961*Y[3]-1308804917.83059*Y[1]; YP[4] := -20553101570465.7*Y[3]+258226577236576.*Y[1]+3397228.85075136*Y[7]-3397228.85075136*Y[8]; YP[6] := -4083471344.37387*Y[5]-3736.95173422945*Y[7]-3736.95173422945*Y[8]; YP[7] := -0.131787399793474e-1*Y[7]+0.142581274070568e-11*Y[8]-2.66759588806373*Y[4]+2425.08717121476*Y[6]; YP[8] := 0.142581274070568e-11*Y[7]-0.131787399793474e-1*Y[8]+2.66759588806373*Y[4]+2425.08717121476*Y[6]; YP[1] := Y[2]; YP[3] := Y[4]; YP[5] := Y[6]; 0 end proc, -1, 0, 0, 0, 0, 0, 0]), ( 11 ) = (Array(1..6, 0..8, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .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, (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, (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, (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, (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}, datatype = float[8], order = C_order)), ( 8 ) = ([Array(1..8, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0}, datatype = float[8], order = C_order), Array(1..8, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0}, datatype = float[8], order = C_order), Array(1..8, {(1) = .0, (2) = -1308804.91783059, (3) = .0, (4) = 258226577236.57602, (5) = .0, (6) = -.0, (7) = .0, (8) = .0}, datatype = float[8], order = C_order)]), ( 9 ) = ([Array(1..8, {(1) = .1, (2) = .1, (3) = .1, (4) = .1, (5) = .1, (6) = .1, (7) = .1, (8) = .1}, datatype = float[8], order = C_order), Array(1..8, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0}, datatype = float[8], order = C_order), Array(1..8, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0}, datatype = float[8], order = C_order), Array(1..8, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0}, datatype = float[8], order = C_order), Array(1..8, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0}, datatype = float[8], order = C_order), Array(1..8, 1..8, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .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, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (3, 8) = .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, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (5, 8) = .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, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (7, 7) = .0, (7, 8) = .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}, datatype = float[8], order = C_order), Array(1..8, 1..8, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .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, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (3, 8) = .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, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (5, 8) = .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, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (7, 7) = .0, (7, 8) = .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}, datatype = float[8], order = C_order), Array(1..8, 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}, datatype = float[8], order = C_order), Array(1..8, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 0, (8) = 0}, datatype = integer[4]), Array(1..8, {(1) = 0.10e-2, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0}, datatype = float[8], order = C_order), Array(1..8, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0}, datatype = float[8], order = C_order), Array(1..8, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0}, datatype = float[8], order = C_order), Array(1..8, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0}, datatype = float[8], order = C_order)]), ( 15 ) = ("rkf45"), ( 14 ) = ([0, 0]), ( 13 ) = (), ( 12 ) = (), ( 20 ) = ([]), ( 16 ) = ([0, 0, 0, []]), ( 17 ) = ([proc (N, X, Y, YP) option `[Y[1] = q1(t), Y[2] = diff(q1(t),t), Y[3] = q2(t), Y[4] = diff(q2(t),t), Y[5] = q3(t), Y[6] = diff(q3(t),t), Y[7] = q4(t), Y[8] = q5(t)]`; YP[2] := 104151386.128961*Y[3]-1308804917.83059*Y[1]; YP[4] := -20553101570465.7*Y[3]+258226577236576.*Y[1]+3397228.85075136*Y[7]-3397228.85075136*Y[8]; YP[6] := -4083471344.37387*Y[5]-3736.95173422945*Y[7]-3736.95173422945*Y[8]; YP[7] := -0.131787399793474e-1*Y[7]+0.142581274070568e-11*Y[8]-2.66759588806373*Y[4]+2425.08717121476*Y[6]; YP[8] := 0.142581274070568e-11*Y[7]-0.131787399793474e-1*Y[8]+2.66759588806373*Y[4]+2425.08717121476*Y[6]; YP[1] := Y[2]; YP[3] := Y[4]; YP[5] := Y[6]; 0 end proc, -1, 0, 0, 0, 0, 0, 0]), ( 18 ) = ([]), ( 19 ) = (0)  ] ))  ] ); _y0 := Array(0..8, {(1) = 0., (2) = 0.1e-2, (3) = 0., (4) = 0., (5) = 0., (6) = 0., (7) = 0., (8) = 0.}); _vmap := array( 1 .. 8, [( 1 ) = (1), ( 2 ) = (2), ( 3 ) = (3), ( 5 ) = (5), ( 4 ) = (4), ( 7 ) = (7), ( 6 ) = (6), ( 8 ) = (8)  ] ); _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); if _par <> [] then `dsolve/numeric/process_parameters`(_n, _pars, _par, _y0) end if; if _ini <> [] then `dsolve/numeric/process_initial`(_n-_ne, _ini, _y0, _pars, _vmap) end if; `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; 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] < 10 and 10 <= _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 10 <= _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] < 10 and 10 < _dtbl[5-_i][4][9] then _dtbl[4] := 5-_i; _i := 5-_i end if; if _dtbl[_i][4][9] < 10 then error "no events to clear" elif _nv < _dtbl[_i][4][9]-10 then error "event error condition cannot be cleared" else _j := _dtbl[_i][4][9]-10; 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] < 10 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 _src = 0 and 10 < _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 10 < _dat[4][9] then if _dat[4][9]-10 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-10 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-10 = _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]-10, 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 10 < _dat[4][9] then if _dat[4][9]-10 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-10 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-10 = _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]-10, 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]; _dat[4][26] := _EnvDSNumericSaveDigits; _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, q1(t), diff(q1(t), t), q2(t), diff(q2(t), t), q3(t), diff(q3(t), t), q4(t), q5(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; _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

(6)

 

 

a := plots:-odeplot(res, [seq([t, (cat(q, i))(t)], i = 5)], 0 .. 0.1e-1, thickness = 3);

PLOT(CURVES(Array(1..201, 1..2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = 0.50e-4, (2, 2) = 0.3934858474430906e-2, (3, 1) = 0.10e-3, (3, 2) = 0.14814720221232995e-1, (4, 1) = 0.15e-3, (4, 2) = 0.30069397012351735e-1, (5, 1) = 0.20e-3, (5, 2) = 0.46092468120666204e-1, (6, 1) = 0.25e-3, (6, 2) = 0.5909086547963376e-1, (7, 1) = 0.30e-3, (7, 2) = 0.6597854620137726e-1, (8, 1) = 0.35e-3, (8, 2) = 0.6510370726978898e-1, (9, 1) = 0.40e-3, (9, 2) = 0.56638180936293525e-1, (10, 1) = 0.45e-3, (10, 2) = 0.42537188795164146e-1, (11, 1) = 0.50e-3, (11, 2) = 0.26079013239174224e-1, (12, 1) = 0.55e-3, (12, 2) = 0.1109277264660928e-1, (13, 1) = 0.60e-3, (13, 2) = 0.1056252940469037e-2, (14, 1) = 0.65e-3, (14, 2) = -0.17234848184033303e-2, (15, 1) = 0.70e-3, (15, 2) = 0.33462071470574265e-2, (16, 1) = 0.75e-3, (16, 2) = 0.15003746992440562e-1, (17, 1) = 0.80e-3, (17, 2) = 0.30430399839215923e-1, (18, 1) = 0.85e-3, (18, 2) = 0.4591429014054406e-1, (19, 1) = 0.90e-3, (19, 2) = 0.5772488725216638e-1, (20, 1) = 0.95e-3, (20, 2) = 0.6299205587125424e-1, (21, 1) = 0.10e-2, (21, 2) = 0.6038245021816248e-1, (22, 1) = 0.105e-2, (22, 2) = 0.5041389748602194e-1, (23, 1) = 0.11e-2, (23, 2) = 0.3533364709706017e-1, (24, 1) = 0.115e-2, (24, 2) = 0.18589147746210715e-1, (25, 1) = 0.12e-2, (25, 2) = 0.4015972356903746e-2, (26, 1) = 0.125e-2, (26, 2) = -0.5065767197305358e-2, (27, 1) = 0.13e-2, (27, 2) = -0.6633636594824042e-2, (28, 1) = 0.135e-2, (28, 2) = -0.4394207741044293e-3, (29, 1) = 0.14e-2, (29, 2) = 0.1193228459393442e-1, (30, 1) = 0.145e-2, (30, 2) = 0.2743728751418456e-1, (31, 1) = 0.15e-2, (31, 2) = 0.42288951143100204e-1, (32, 1) = 0.155e-2, (32, 2) = 0.5285030707162522e-1, (33, 1) = 0.16e-2, (33, 2) = 0.5649110156809198e-1, (34, 1) = 0.165e-2, (34, 2) = 0.5220769136296411e-1, (35, 1) = 0.17e-2, (35, 2) = 0.4085980268638853e-1, (36, 1) = 0.175e-2, (36, 2) = 0.2496830509640725e-1, (37, 1) = 0.18e-2, (37, 2) = 0.8121555722465477e-2, (38, 1) = 0.185e-2, (38, 2) = -0.5869799360406876e-2, (39, 1) = 0.19e-2, (39, 2) = -0.13870512552222167e-1, (40, 1) = 0.195e-2, (40, 2) = -0.1415942187442424e-1, (41, 1) = 0.20e-2, (41, 2) = -0.6835030956277502e-2, (42, 1) = 0.205e-2, (42, 2) = 0.6207574792327089e-2, (43, 1) = 0.21e-2, (43, 2) = 0.21723140996709883e-1, (44, 1) = 0.215e-2, (44, 2) = 0.35880777515398345e-1, (45, 1) = 0.22e-2, (45, 2) = 0.4516662888377902e-1, (46, 1) = 0.225e-2, (46, 2) = 0.4721190910839272e-1, (47, 1) = 0.23e-2, (47, 2) = 0.4135127623956298e-1, (48, 1) = 0.235e-2, (48, 2) = 0.28779929111276206e-1, (49, 1) = 0.24e-2, (49, 2) = 0.12272343220495698e-1, (50, 1) = 0.245e-2, (50, 2) = -0.44711045370253175e-2, (51, 1) = 0.25e-2, (51, 2) = -0.1769576226550336e-1, (52, 1) = 0.255e-2, (52, 2) = -0.2447718848059602e-1, (53, 1) = 0.26e-2, (53, 2) = -0.23410182526608328e-1, (54, 1) = 0.265e-2, (54, 2) = -0.14939904232865578e-1, (55, 1) = 0.27e-2, (55, 2) = -0.1257085601848231e-2, (56, 1) = 0.275e-2, (56, 2) = 0.14218035950823939e-1, (57, 1) = 0.28e-2, (57, 2) = 0.27641580993279923e-1, (58, 1) = 0.285e-2, (58, 2) = 0.3565171068997031e-1, (59, 1) = 0.29e-2, (59, 2) = 0.3616094106275799e-1, (60, 1) = 0.295e-2, (60, 2) = 0.2884824646010692e-1, (61, 1) = 0.30e-2, (61, 2) = 0.15235029853583918e-1, (62, 1) = 0.305e-2, (62, 2) = -0.16729803376715788e-2, (63, 1) = 0.31e-2, (63, 2) = -0.1809362864744564e-1, (64, 1) = 0.315e-2, (64, 2) = -0.3035917112172065e-1, (65, 1) = 0.32e-2, (65, 2) = -0.35780369613793266e-1, (66, 1) = 0.325e-2, (66, 2) = -0.3328005303315349e-1, (67, 1) = 0.33e-2, (67, 2) = -0.2364698467247254e-1, (68, 1) = 0.335e-2, (68, 2) = -0.9350103196722998e-2, (69, 1) = 0.34e-2, (69, 2) = 0.6043123873608723e-2, (70, 1) = 0.345e-2, (70, 2) = 0.18707220106800905e-1, (71, 1) = 0.35e-2, (71, 2) = 0.25460104865689916e-1, (72, 1) = 0.355e-2, (72, 2) = 0.2451305645053763e-1, (73, 1) = 0.36e-2, (73, 2) = 0.15892423184357206e-1, (74, 1) = 0.365e-2, (74, 2) = 0.14337704201340467e-2, (75, 1) = 0.37e-2, (75, 2) = -0.156502728437588e-1, (76, 1) = 0.375e-2, (76, 2) = -0.3152662710762403e-1, (77, 1) = 0.38e-2, (77, 2) = -0.4264467841759113e-1, (78, 1) = 0.385e-2, (78, 2) = -0.46572746607888856e-1, (79, 1) = 0.39e-2, (79, 2) = -0.4257102248310031e-1, (80, 1) = 0.395e-2, (80, 2) = -0.31765953394425034e-1, (81, 1) = 0.40e-2, (81, 2) = -0.16884946767315334e-1, (82, 1) = 0.405e-2, (82, 2) = -0.16138457392678891e-2, (83, 1) = 0.41e-2, (83, 2) = 0.10271499426385512e-1, (84, 1) = 0.415e-2, (84, 2) = 0.15794939297596743e-1, (85, 1) = 0.42e-2, (85, 2) = 0.13481478248944504e-1, (86, 1) = 0.425e-2, (86, 2) = 0.37050715366142074e-2, (87, 1) = 0.43e-2, (87, 2) = -0.11399135815015168e-1, (88, 1) = 0.435e-2, (88, 2) = -0.2843754338300747e-1, (89, 1) = 0.44e-2, (89, 2) = -0.4355740079845767e-1, (90, 1) = 0.445e-2, (90, 2) = -0.5335439723246622e-1, (91, 1) = 0.45e-2, (91, 2) = -0.5567471096927273e-1, (92, 1) = 0.455e-2, (92, 2) = -0.5012251651889939e-1, (93, 1) = 0.46e-2, (93, 2) = -0.3815337708704378e-1, (94, 1) = 0.465e-2, (94, 2) = -0.2273141297921697e-1, (95, 1) = 0.47e-2, (95, 2) = -0.763101264642147e-2, (96, 1) = 0.475e-2, (96, 2) = 0.345244457034857e-2, (97, 1) = 0.48e-2, (97, 2) = 0.7773397506905774e-2, (98, 1) = 0.485e-2, (98, 2) = 0.4183180122737466e-2, (99, 1) = 0.49e-2, (99, 2) = -0.6599057892024972e-2, (100, 1) = 0.495e-2, (100, 2) = -0.2215548665038469e-1, (101, 1) = 0.50e-2, (101, 2) = -0.3893902060538723e-1, (102, 1) = 0.505e-2, (102, 2) = -0.5310885704546906e-1, (103, 1) = 0.51e-2, (103, 2) = -0.6143534314219014e-1, (104, 1) = 0.515e-2, (104, 2) = -0.6206087192288756e-1, (105, 1) = 0.52e-2, (105, 2) = -0.5493766961105571e-1, (106, 1) = 0.525e-2, (106, 2) = -0.4183912208446165e-1, (107, 1) = 0.53e-2, (107, 2) = -0.25942033831557153e-1, (108, 1) = 0.535e-2, (108, 2) = -0.11078311642077229e-1, (109, 1) = 0.54e-2, (109, 2) = -0.8321737981824337e-3, (110, 1) = 0.545e-2, (110, 2) = 0.230444163142728e-2, (111, 1) = 0.55e-2, (111, 2) = -0.2480897690073637e-2, (112, 1) = 0.555e-2, (112, 2) = -0.14129440538039394e-1, (113, 1) = 0.56e-2, (113, 2) = -0.29960435409614152e-1, (114, 1) = 0.565e-2, (114, 2) = -0.46302510670876255e-1, (115, 1) = 0.57e-2, (115, 2) = -0.5935847772954657e-1, (116, 1) = 0.575e-2, (116, 2) = -0.6609996736195842e-1, (117, 1) = 0.58e-2, (117, 2) = -0.6498092917382291e-1, (118, 1) = 0.585e-2, (118, 2) = -0.5630201466793459e-1, (119, 1) = 0.59e-2, (119, 2) = -0.4214006521942725e-1, (120, 1) = 0.595e-2, (120, 2) = -0.25858965245355605e-1, (121, 1) = 0.60e-2, (121, 2) = -0.11317232163687194e-1, (122, 1) = 0.605e-2, (122, 2) = -0.19589773068628843e-2, (123, 1) = 0.61e-2, (123, 2) = -0.23567354077730286e-5, (124, 1) = 0.615e-2, (124, 2) = -0.5916777131038856e-2, (125, 1) = 0.62e-2, (125, 2) = -0.18312073640741944e-1, (126, 1) = 0.625e-2, (126, 2) = -0.3426580408435659e-1, (127, 1) = 0.63e-2, (127, 2) = -0.5001159218552262e-1, (128, 1) = 0.635e-2, (128, 2) = -0.6182642623041382e-1, (129, 1) = 0.64e-2, (129, 2) = -0.669078506867298e-1, (130, 1) = 0.645e-2, (130, 2) = -0.6403438921758917e-1, (131, 1) = 0.65e-2, (131, 2) = -0.5385356102867506e-1, (132, 1) = 0.655e-2, (132, 2) = -0.38729577732612874e-1, (133, 1) = 0.66e-2, (133, 2) = -0.2218657112496857e-1, (134, 1) = 0.665e-2, (134, 2) = -0.8078494331558371e-2, (135, 1) = 0.67e-2, (135, 2) = 0.318923204061004e-3, (136, 1) = 0.675e-2, (136, 2) = 0.10800295929919244e-2, (137, 1) = 0.68e-2, (137, 2) = -0.5916900375677731e-2, (138, 1) = 0.685e-2, (138, 2) = -0.18960809410312043e-1, (139, 1) = 0.69e-2, (139, 2) = -0.3491083068661165e-1, (140, 1) = 0.695e-2, (140, 2) = -0.49936166429364166e-1, (141, 1) = 0.70e-2, (141, 2) = -0.604187060755389e-1, (142, 1) = 0.705e-2, (142, 2) = -0.6380552135296715e-1, (143, 1) = 0.71e-2, (143, 2) = -0.5921058597934421e-1, (144, 1) = 0.715e-2, (144, 2) = -0.47623782069682534e-1, (145, 1) = 0.72e-2, (145, 2) = -0.3167792393935585e-1, (146, 1) = 0.725e-2, (146, 2) = -0.1502866790307938e-1, (147, 1) = 0.73e-2, (147, 2) = -0.14934003733594885e-2, (148, 1) = 0.735e-2, (148, 2) = 0.5848153939460289e-2, (149, 1) = 0.74e-2, (149, 2) = 0.5379507672383767e-2, (150, 1) = 0.745e-2, (150, 2) = -0.2671652635818875e-2, (151, 1) = 0.75e-2, (151, 2) = -0.16287017380720352e-1, (152, 1) = 0.755e-2, (152, 2) = -0.3213306188294428e-1, (153, 1) = 0.76e-2, (153, 2) = -0.46346343611441215e-1, (154, 1) = 0.765e-2, (154, 2) = -0.55443801347084404e-1, (155, 1) = 0.77e-2, (155, 2) = -0.5714351103109579e-1, (156, 1) = 0.775e-2, (156, 2) = -0.5090253405598848e-1, (157, 1) = 0.78e-2, (157, 2) = -0.380451561405412e-1, (158, 1) = 0.785e-2, (158, 2) = -0.21451188606688994e-1, (159, 1) = 0.79e-2, (159, 2) = -0.4877734861563436e-2, (160, 1) = 0.795e-2, (160, 2) = 0.792576959599106e-2, (161, 1) = 0.80e-2, (161, 2) = 0.14100913720697108e-1, (162, 1) = 0.805e-2, (162, 2) = 0.12353728975264577e-1, (163, 1) = 0.81e-2, (163, 2) = 0.32596789476206883e-2, (164, 1) = 0.815e-2, (164, 2) = -0.10871812566678232e-1, (165, 1) = 0.82e-2, (165, 2) = -0.26541389699127827e-1, (166, 1) = 0.825e-2, (166, 2) = -0.398842015613804e-1, (167, 1) = 0.83e-2, (167, 2) = -0.47580567710252944e-1, (168, 1) = 0.835e-2, (168, 2) = -0.4763832210603971e-1, (169, 1) = 0.84e-2, (169, 2) = -0.3986246404441548e-1, (170, 1) = 0.845e-2, (170, 2) = -0.2590143338951813e-1, (171, 1) = 0.85e-2, (171, 2) = -0.8859068162329637e-2, (172, 1) = 0.855e-2, (172, 2) = 0.7436402046650333e-2, (173, 1) = 0.86e-2, (173, 2) = 0.19334108685655733e-1, (174, 1) = 0.865e-2, (174, 2) = 0.2422062731899008e-1, (175, 1) = 0.87e-2, (175, 2) = 0.21135743449099634e-1, (176, 1) = 0.875e-2, (176, 2) = 0.10998753757843453e-1, (177, 1) = 0.88e-2, (177, 2) = -0.3608033904126598e-2, (178, 1) = 0.885e-2, (178, 2) = -0.1904766018502611e-1, (179, 1) = 0.89e-2, (179, 2) = -0.3148538138915938e-1, (180, 1) = 0.895e-2, (180, 2) = -0.3779233517471633e-1, (181, 1) = 0.90e-2, (181, 2) = -0.3628291482759238e-1, (182, 1) = 0.905e-2, (182, 2) = -0.27112221534077018e-1, (183, 1) = 0.91e-2, (183, 2) = -0.12239871890483962e-1, (184, 1) = 0.915e-2, (184, 2) = 0.5031370121267965e-2, (185, 1) = 0.92e-2, (185, 2) = 0.2083346262594309e-1, (186, 1) = 0.925e-2, (186, 2) = 0.31644251458152736e-1, (187, 1) = 0.93e-2, (187, 2) = 0.3511721136177279e-1, (188, 1) = 0.935e-2, (188, 2) = 0.30634335595166096e-1, (189, 1) = 0.94e-2, (189, 2) = 0.19451816230380184e-1, (190, 1) = 0.945e-2, (190, 2) = 0.4404143480168701e-2, (191, 1) = 0.95e-2, (191, 2) = -0.10763641738640067e-1, (192, 1) = 0.955e-2, (192, 2) = -0.22278388031127704e-1, (193, 1) = 0.96e-2, (193, 2) = -0.2722788975349196e-1, (194, 1) = 0.965e-2, (194, 2) = -0.24247310194820158e-1, (195, 1) = 0.97e-2, (195, 2) = -0.13841039821944007e-1, (196, 1) = 0.975e-2, (196, 2) = 0.17357885741804994e-2, (197, 1) = 0.98e-2, (197, 2) = 0.19008304248345837e-1, (198, 1) = 0.985e-2, (198, 2) = 0.3410033297989134e-1, (199, 1) = 0.99e-2, (199, 2) = 0.4364746542498778e-1, (200, 1) = 0.995e-2, (200, 2) = 0.4558971296998513e-1, (201, 1) = 0.1e-1, (201, 2) = 0.39656868730009724e-1}, datatype = float[8], order = C_order), COLOUR(RGB, .47058824, 0., 0.54901961e-1)), THICKNESS(3), AXESLABELS(t, q5))

(7)

a

 

XY := plottools:-getdata(a)[3]

XY := Matrix(201, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = 0.50e-4, (2, 2) = 0.3934858474430906e-2, (3, 1) = 0.10e-3, (3, 2) = 0.14814720221232995e-1, (4, 1) = 0.15e-3, (4, 2) = 0.30069397012351735e-1, (5, 1) = 0.20e-3, (5, 2) = 0.46092468120666204e-1, (6, 1) = 0.25e-3, (6, 2) = 0.5909086547963376e-1, (7, 1) = 0.30e-3, (7, 2) = 0.6597854620137726e-1, (8, 1) = 0.35e-3, (8, 2) = 0.6510370726978898e-1, (9, 1) = 0.40e-3, (9, 2) = 0.56638180936293525e-1, (10, 1) = 0.45e-3, (10, 2) = 0.42537188795164146e-1, (11, 1) = 0.50e-3, (11, 2) = 0.26079013239174224e-1, (12, 1) = 0.55e-3, (12, 2) = 0.1109277264660928e-1, (13, 1) = 0.60e-3, (13, 2) = 0.1056252940469037e-2, (14, 1) = 0.65e-3, (14, 2) = -0.17234848184033303e-2, (15, 1) = 0.70e-3, (15, 2) = 0.33462071470574265e-2, (16, 1) = 0.75e-3, (16, 2) = 0.15003746992440562e-1, (17, 1) = 0.80e-3, (17, 2) = 0.30430399839215923e-1, (18, 1) = 0.85e-3, (18, 2) = 0.4591429014054406e-1, (19, 1) = 0.90e-3, (19, 2) = 0.5772488725216638e-1, (20, 1) = 0.95e-3, (20, 2) = 0.6299205587125424e-1, (21, 1) = 0.10e-2, (21, 2) = 0.6038245021816248e-1, (22, 1) = 0.105e-2, (22, 2) = 0.5041389748602194e-1, (23, 1) = 0.11e-2, (23, 2) = 0.3533364709706017e-1, (24, 1) = 0.115e-2, (24, 2) = 0.18589147746210715e-1, (25, 1) = 0.12e-2, (25, 2) = 0.4015972356903746e-2, (26, 1) = 0.125e-2, (26, 2) = -0.5065767197305358e-2, (27, 1) = 0.13e-2, (27, 2) = -0.6633636594824042e-2, (28, 1) = 0.135e-2, (28, 2) = -0.4394207741044293e-3, (29, 1) = 0.14e-2, (29, 2) = 0.1193228459393442e-1, (30, 1) = 0.145e-2, (30, 2) = 0.2743728751418456e-1, (31, 1) = 0.15e-2, (31, 2) = 0.42288951143100204e-1, (32, 1) = 0.155e-2, (32, 2) = 0.5285030707162522e-1, (33, 1) = 0.16e-2, (33, 2) = 0.5649110156809198e-1, (34, 1) = 0.165e-2, (34, 2) = 0.5220769136296411e-1, (35, 1) = 0.17e-2, (35, 2) = 0.4085980268638853e-1, (36, 1) = 0.175e-2, (36, 2) = 0.2496830509640725e-1, (37, 1) = 0.18e-2, (37, 2) = 0.8121555722465477e-2, (38, 1) = 0.185e-2, (38, 2) = -0.5869799360406876e-2, (39, 1) = 0.19e-2, (39, 2) = -0.13870512552222167e-1, (40, 1) = 0.195e-2, (40, 2) = -0.1415942187442424e-1, (41, 1) = 0.20e-2, (41, 2) = -0.6835030956277502e-2, (42, 1) = 0.205e-2, (42, 2) = 0.6207574792327089e-2, (43, 1) = 0.21e-2, (43, 2) = 0.21723140996709883e-1, (44, 1) = 0.215e-2, (44, 2) = 0.35880777515398345e-1, (45, 1) = 0.22e-2, (45, 2) = 0.4516662888377902e-1, (46, 1) = 0.225e-2, (46, 2) = 0.4721190910839272e-1, (47, 1) = 0.23e-2, (47, 2) = 0.4135127623956298e-1, (48, 1) = 0.235e-2, (48, 2) = 0.28779929111276206e-1, (49, 1) = 0.24e-2, (49, 2) = 0.12272343220495698e-1, (50, 1) = 0.245e-2, (50, 2) = -0.44711045370253175e-2, (51, 1) = 0.25e-2, (51, 2) = -0.1769576226550336e-1, (52, 1) = 0.255e-2, (52, 2) = -0.2447718848059602e-1, (53, 1) = 0.26e-2, (53, 2) = -0.23410182526608328e-1, (54, 1) = 0.265e-2, (54, 2) = -0.14939904232865578e-1, (55, 1) = 0.27e-2, (55, 2) = -0.1257085601848231e-2, (56, 1) = 0.275e-2, (56, 2) = 0.14218035950823939e-1, (57, 1) = 0.28e-2, (57, 2) = 0.27641580993279923e-1, (58, 1) = 0.285e-2, (58, 2) = 0.3565171068997031e-1, (59, 1) = 0.29e-2, (59, 2) = 0.3616094106275799e-1, (60, 1) = 0.295e-2, (60, 2) = 0.2884824646010692e-1, (61, 1) = 0.30e-2, (61, 2) = 0.15235029853583918e-1, (62, 1) = 0.305e-2, (62, 2) = -0.16729803376715788e-2, (63, 1) = 0.31e-2, (63, 2) = -0.1809362864744564e-1, (64, 1) = 0.315e-2, (64, 2) = -0.3035917112172065e-1, (65, 1) = 0.32e-2, (65, 2) = -0.35780369613793266e-1, (66, 1) = 0.325e-2, (66, 2) = -0.3328005303315349e-1, (67, 1) = 0.33e-2, (67, 2) = -0.2364698467247254e-1, (68, 1) = 0.335e-2, (68, 2) = -0.9350103196722998e-2, (69, 1) = 0.34e-2, (69, 2) = 0.6043123873608723e-2, (70, 1) = 0.345e-2, (70, 2) = 0.18707220106800905e-1, (71, 1) = 0.35e-2, (71, 2) = 0.25460104865689916e-1, (72, 1) = 0.355e-2, (72, 2) = 0.2451305645053763e-1, (73, 1) = 0.36e-2, (73, 2) = 0.15892423184357206e-1, (74, 1) = 0.365e-2, (74, 2) = 0.14337704201340467e-2, (75, 1) = 0.37e-2, (75, 2) = -0.156502728437588e-1, (76, 1) = 0.375e-2, (76, 2) = -0.3152662710762403e-1, (77, 1) = 0.38e-2, (77, 2) = -0.4264467841759113e-1, (78, 1) = 0.385e-2, (78, 2) = -0.46572746607888856e-1, (79, 1) = 0.39e-2, (79, 2) = -0.4257102248310031e-1, (80, 1) = 0.395e-2, (80, 2) = -0.31765953394425034e-1, (81, 1) = 0.40e-2, (81, 2) = -0.16884946767315334e-1, (82, 1) = 0.405e-2, (82, 2) = -0.16138457392678891e-2, (83, 1) = 0.41e-2, (83, 2) = 0.10271499426385512e-1, (84, 1) = 0.415e-2, (84, 2) = 0.15794939297596743e-1, (85, 1) = 0.42e-2, (85, 2) = 0.13481478248944504e-1, (86, 1) = 0.425e-2, (86, 2) = 0.37050715366142074e-2, (87, 1) = 0.43e-2, (87, 2) = -0.11399135815015168e-1, (88, 1) = 0.435e-2, (88, 2) = -0.2843754338300747e-1, (89, 1) = 0.44e-2, (89, 2) = -0.4355740079845767e-1, (90, 1) = 0.445e-2, (90, 2) = -0.5335439723246622e-1, (91, 1) = 0.45e-2, (91, 2) = -0.5567471096927273e-1, (92, 1) = 0.455e-2, (92, 2) = -0.5012251651889939e-1, (93, 1) = 0.46e-2, (93, 2) = -0.3815337708704378e-1, (94, 1) = 0.465e-2, (94, 2) = -0.2273141297921697e-1, (95, 1) = 0.47e-2, (95, 2) = -0.763101264642147e-2, (96, 1) = 0.475e-2, (96, 2) = 0.345244457034857e-2, (97, 1) = 0.48e-2, (97, 2) = 0.7773397506905774e-2, (98, 1) = 0.485e-2, (98, 2) = 0.4183180122737466e-2, (99, 1) = 0.49e-2, (99, 2) = -0.6599057892024972e-2, (100, 1) = 0.495e-2, (100, 2) = -0.2215548665038469e-1, (101, 1) = 0.50e-2, (101, 2) = -0.3893902060538723e-1, (102, 1) = 0.505e-2, (102, 2) = -0.5310885704546906e-1, (103, 1) = 0.51e-2, (103, 2) = -0.6143534314219014e-1, (104, 1) = 0.515e-2, (104, 2) = -0.6206087192288756e-1, (105, 1) = 0.52e-2, (105, 2) = -0.5493766961105571e-1, (106, 1) = 0.525e-2, (106, 2) = -0.4183912208446165e-1, (107, 1) = 0.53e-2, (107, 2) = -0.25942033831557153e-1, (108, 1) = 0.535e-2, (108, 2) = -0.11078311642077229e-1, (109, 1) = 0.54e-2, (109, 2) = -0.8321737981824337e-3, (110, 1) = 0.545e-2, (110, 2) = 0.230444163142728e-2, (111, 1) = 0.55e-2, (111, 2) = -0.2480897690073637e-2, (112, 1) = 0.555e-2, (112, 2) = -0.14129440538039394e-1, (113, 1) = 0.56e-2, (113, 2) = -0.29960435409614152e-1, (114, 1) = 0.565e-2, (114, 2) = -0.46302510670876255e-1, (115, 1) = 0.57e-2, (115, 2) = -0.5935847772954657e-1, (116, 1) = 0.575e-2, (116, 2) = -0.6609996736195842e-1, (117, 1) = 0.58e-2, (117, 2) = -0.6498092917382291e-1, (118, 1) = 0.585e-2, (118, 2) = -0.5630201466793459e-1, (119, 1) = 0.59e-2, (119, 2) = -0.4214006521942725e-1, (120, 1) = 0.595e-2, (120, 2) = -0.25858965245355605e-1, (121, 1) = 0.60e-2, (121, 2) = -0.11317232163687194e-1, (122, 1) = 0.605e-2, (122, 2) = -0.19589773068628843e-2, (123, 1) = 0.61e-2, (123, 2) = -0.23567354077730286e-5, (124, 1) = 0.615e-2, (124, 2) = -0.5916777131038856e-2, (125, 1) = 0.62e-2, (125, 2) = -0.18312073640741944e-1, (126, 1) = 0.625e-2, (126, 2) = -0.3426580408435659e-1, (127, 1) = 0.63e-2, (127, 2) = -0.5001159218552262e-1, (128, 1) = 0.635e-2, (128, 2) = -0.6182642623041382e-1, (129, 1) = 0.64e-2, (129, 2) = -0.669078506867298e-1, (130, 1) = 0.645e-2, (130, 2) = -0.6403438921758917e-1, (131, 1) = 0.65e-2, (131, 2) = -0.5385356102867506e-1, (132, 1) = 0.655e-2, (132, 2) = -0.38729577732612874e-1, (133, 1) = 0.66e-2, (133, 2) = -0.2218657112496857e-1, (134, 1) = 0.665e-2, (134, 2) = -0.8078494331558371e-2, (135, 1) = 0.67e-2, (135, 2) = 0.318923204061004e-3, (136, 1) = 0.675e-2, (136, 2) = 0.10800295929919244e-2, (137, 1) = 0.68e-2, (137, 2) = -0.5916900375677731e-2, (138, 1) = 0.685e-2, (138, 2) = -0.18960809410312043e-1, (139, 1) = 0.69e-2, (139, 2) = -0.3491083068661165e-1, (140, 1) = 0.695e-2, (140, 2) = -0.49936166429364166e-1, (141, 1) = 0.70e-2, (141, 2) = -0.604187060755389e-1, (142, 1) = 0.705e-2, (142, 2) = -0.6380552135296715e-1, (143, 1) = 0.71e-2, (143, 2) = -0.5921058597934421e-1, (144, 1) = 0.715e-2, (144, 2) = -0.47623782069682534e-1, (145, 1) = 0.72e-2, (145, 2) = -0.3167792393935585e-1, (146, 1) = 0.725e-2, (146, 2) = -0.1502866790307938e-1, (147, 1) = 0.73e-2, (147, 2) = -0.14934003733594885e-2, (148, 1) = 0.735e-2, (148, 2) = 0.5848153939460289e-2, (149, 1) = 0.74e-2, (149, 2) = 0.5379507672383767e-2, (150, 1) = 0.745e-2, (150, 2) = -0.2671652635818875e-2, (151, 1) = 0.75e-2, (151, 2) = -0.16287017380720352e-1, (152, 1) = 0.755e-2, (152, 2) = -0.3213306188294428e-1, (153, 1) = 0.76e-2, (153, 2) = -0.46346343611441215e-1, (154, 1) = 0.765e-2, (154, 2) = -0.55443801347084404e-1, (155, 1) = 0.77e-2, (155, 2) = -0.5714351103109579e-1, (156, 1) = 0.775e-2, (156, 2) = -0.5090253405598848e-1, (157, 1) = 0.78e-2, (157, 2) = -0.380451561405412e-1, (158, 1) = 0.785e-2, (158, 2) = -0.21451188606688994e-1, (159, 1) = 0.79e-2, (159, 2) = -0.4877734861563436e-2, (160, 1) = 0.795e-2, (160, 2) = 0.792576959599106e-2, (161, 1) = 0.80e-2, (161, 2) = 0.14100913720697108e-1, (162, 1) = 0.805e-2, (162, 2) = 0.12353728975264577e-1, (163, 1) = 0.81e-2, (163, 2) = 0.32596789476206883e-2, (164, 1) = 0.815e-2, (164, 2) = -0.10871812566678232e-1, (165, 1) = 0.82e-2, (165, 2) = -0.26541389699127827e-1, (166, 1) = 0.825e-2, (166, 2) = -0.398842015613804e-1, (167, 1) = 0.83e-2, (167, 2) = -0.47580567710252944e-1, (168, 1) = 0.835e-2, (168, 2) = -0.4763832210603971e-1, (169, 1) = 0.84e-2, (169, 2) = -0.3986246404441548e-1, (170, 1) = 0.845e-2, (170, 2) = -0.2590143338951813e-1, (171, 1) = 0.85e-2, (171, 2) = -0.8859068162329637e-2, (172, 1) = 0.855e-2, (172, 2) = 0.7436402046650333e-2, (173, 1) = 0.86e-2, (173, 2) = 0.19334108685655733e-1, (174, 1) = 0.865e-2, (174, 2) = 0.2422062731899008e-1, (175, 1) = 0.87e-2, (175, 2) = 0.21135743449099634e-1, (176, 1) = 0.875e-2, (176, 2) = 0.10998753757843453e-1, (177, 1) = 0.88e-2, (177, 2) = -0.3608033904126598e-2, (178, 1) = 0.885e-2, (178, 2) = -0.1904766018502611e-1, (179, 1) = 0.89e-2, (179, 2) = -0.3148538138915938e-1, (180, 1) = 0.895e-2, (180, 2) = -0.3779233517471633e-1, (181, 1) = 0.90e-2, (181, 2) = -0.3628291482759238e-1, (182, 1) = 0.905e-2, (182, 2) = -0.27112221534077018e-1, (183, 1) = 0.91e-2, (183, 2) = -0.12239871890483962e-1, (184, 1) = 0.915e-2, (184, 2) = 0.5031370121267965e-2, (185, 1) = 0.92e-2, (185, 2) = 0.2083346262594309e-1, (186, 1) = 0.925e-2, (186, 2) = 0.31644251458152736e-1, (187, 1) = 0.93e-2, (187, 2) = 0.3511721136177279e-1, (188, 1) = 0.935e-2, (188, 2) = 0.30634335595166096e-1, (189, 1) = 0.94e-2, (189, 2) = 0.19451816230380184e-1, (190, 1) = 0.945e-2, (190, 2) = 0.4404143480168701e-2, (191, 1) = 0.95e-2, (191, 2) = -0.10763641738640067e-1, (192, 1) = 0.955e-2, (192, 2) = -0.22278388031127704e-1, (193, 1) = 0.96e-2, (193, 2) = -0.2722788975349196e-1, (194, 1) = 0.965e-2, (194, 2) = -0.24247310194820158e-1, (195, 1) = 0.97e-2, (195, 2) = -0.13841039821944007e-1, (196, 1) = 0.975e-2, (196, 2) = 0.17357885741804994e-2, (197, 1) = 0.98e-2, (197, 2) = 0.19008304248345837e-1, (198, 1) = 0.985e-2, (198, 2) = 0.3410033297989134e-1, (199, 1) = 0.99e-2, (199, 2) = 0.4364746542498778e-1, (200, 1) = 0.995e-2, (200, 2) = 0.4558971296998513e-1, (201, 1) = 0.1e-1, (201, 2) = 0.39656868730009724e-1}, datatype = float[8], order = C_order)

(8)

with(Statistics):

``

f := DirectSearch:-DataFit(A*cos(omega1*x+phi1)*sin(omega2*x), XY[() .. (), 1], XY[() .. (), 2], x, initialpoint = [A = 0.5e-1, omega1 = evalf(2*Pi/(0.1e-1)), omega2 = 10*evalf(2*Pi/(0.1e-1)), phi1 = 0], fitmethod = lms)

[HFloat(1.6381997662567137e-8), [A = HFloat(-0.06724203423372291), omega1 = HFloat(-4647.2817247860985), omega2 = HFloat(5158.3386926920375), phi1 = HFloat(-1.5702941306139961)], 3427]

(9)

``

display([a, plot(eval(A*cos(omega1*x+phi1)*sin(omega2*x), f[2]), x = 0 .. 0.1e-1, color = blue)])

``

Download DataFit.mw

By change

March 30 2014 Markiyan Hirnyk 5673
0 21

Your w is piecewise concerning y=(x-a)/t in fact. Making use of that, we obtain


restart; w := piecewise((x-a)/t <= -10, 202*a-200*x-(202001/101)*t, (x-a)/t <= -910/101, 3*a-x-(1011/101)*t, (x-a)/t <= 910/101, 2*a-t, (x-a)/t <= 10, a+x-(1011/101)*t, 10 < (x-a)/t, -198*a+200*x-(202001/101)*t)

ww := eval(w, [y = (x-a)/t, x = t*y+a])

piecewise(y <= -10, 2*a-200*t*y-(202001/101)*t, y <= -910/101, 2*a-t*y-(1011/101)*t, y <= 910/101, 2*a-t, y <= 10, 2*a+t*y-(1011/101)*t, 10 < y, 2*a+200*t*y-(202001/101)*t)

(1)

www := eval(ww, a = -1)

piecewise(y <= -10, -2-200*t*y-(202001/101)*t, y <= -910/101, -2-t*y-(1011/101)*t, y <= 910/101, -2-t, y <= 10, -2+t*y-(1011/101)*t, 10 < y, -2+200*t*y-(202001/101)*t)

(2)

wwww := eval(eval(www, [y = (x-a)/t]), a = -1)

piecewise((x+1)/t <= -10, -202-200*x-(202001/101)*t, (x+1)/t <= -910/101, -3-x-(1011/101)*t, (x+1)/t <= 910/101, -2-t, (x+1)/t <= 10, -1+x-(1011/101)*t, 10 < (x+1)/t, 198+200*x-(202001/101)*t)

(3)

plot3d(wwww, x = -4 .. 4, t = 0 .. 4)

 

``

 

 

``


Download piecewise.mw

Yes

March 29 2014 Markiyan Hirnyk 5673
1 2

Without loss of generality we may assume h=1.  Putting n=4, we obtain

 

restart; ODE := diff((-(diff(u(y), y)))^4, y) = A; bcs := (D(u))(0) = 0, u(1) = 0; dsolve({ODE, bcs})

u(y) = -(4/5)*y*(A*y)^(1/4)+(4/5)*A^(1/4), u(y) = (4/5)*y*(A*y)^(1/4)-(4/5)*A^(1/4), u(y) = -((4/5)*I)*y*(A*y)^(1/4)+((4/5)*I)*A^(1/4), u(y) = ((4/5)*I)*y*(A*y)^(1/4)-((4/5)*I)*A^(1/4)

(1)

``

``

Putting  n=5, we obtain

In view of the above, we define

test1.mw

Download nonzero.mw

Edit. The last three commands.

 

By select

March 26 2014 Markiyan Hirnyk 5673
0 1

How about this?

F := -(int(del_u0(x)*(diff(N_xx(x), x)), x = 0 .. L))+del_u0(L)*N_xx(L)-del_u0(0)*N_xx(0)+ibp2+ibp3:

select(has, F, int);

As far as I remember it, a similar question was asked and answered. I can't find a reference in short time.

 

Reference

March 25 2014 Markiyan Hirnyk 5673
1 1

See http://www.mapleprimes.com/questions/142211-Correct-Upto-7-Decimal-Figurs-not-Significant-Digits

Don't hesitate to ask for further explanation in need.

PS. This link can be found by the "digits" search in MaplePrimes at the top of this page.

By convert,piecewise

March 24 2014 Markiyan Hirnyk 5673
1 0

This can be done as follows.

 

restart;
w123 := convert(c1*r*Heaviside(r-a), piecewise, r)+c2*r;
simplify(combine(int(r*(int((diff(w123, r))^2/r, r)), r)), size) assuming 0< r <lambda and a<lambda and 0<a and 0<lambda

simplification.mw

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