How to make this code run?

abdulganiy — Sun, 17 May 2026 16:26:57 Z

restart;

with(plots): with(LinearAlgebra):

# TFSB Coefficients (symbolic in u)

beta0 := u -> (sin(u)*u^3 - 12*u^2 - 24*cos(u) + 24)/(12*(sin(u)*u + 2*cos(u) - 2)*u^2):

beta1 := u -> (5*sin(u)*u^3 + 12*cos(u)*u^2 + 24*cos(u) - 24)/(6*(sin(u)*u + 2*cos(u) - 2)*u^2):

beta2 := u -> beta0(u):

rho0 := u -> ((-u^2-12)*cos(u) - 5*u^2 + 12)/(12*(sin(u)*u + 2*cos(u) - 2)*u^2):

rho1 := u -> (-7*cos(u)*u^3 + 27*sin(u)*u^2 + 120*sin(u) - 120*u)/(60*u^2*(cos(u)*u + 2*u - 3*sin(u))):

rho2 := u -> -rho0(u):

# Secondary coefficients (simplified versions)

beta00 := u -> 13/42 - 9*u^2/7840:

beta10 := u -> 1/6 + u^2/720:

beta20 := u -> 1/42 - 17*u^2/70560:

beta01 := u -> 187/1680 + 611*u^2/705600:

beta11 := u -> 11/30 - 29*u^2/25200:

beta21 := u -> 37/1680 + 67*u^2/235200:

beta02 := u -> 11/70 + 491*u^2/352800:

beta12 := u -> 9/10 - 31*u^2/8400:

beta22 := u -> 31/70 + 811*u^2/352800:

rho01 := u -> 2/105 + 407*u^2/1058400:

rho11 := u -> -19/210 + 41*u^2/105840:

rho21 := u -> -1/168 - 101*u^2/529200:

rho02 := u -> 53/1680 + 1633*u^2/2116800:

rho12 := u -> 8/105 - 4*u^2/6615:

rho22 := u -> -101/1680 - 2273*u^2/2116800:

# Problem definition

omega := 1:

epsilon := 3*Pi/2:

phi := x -> 3*sin(x) - 5*cos(x): # history function

f := (x, v, vp, vd) -> -v - vd + 3*cos(x) + 5*sin(x):

g := proc(x, v, vp, vd, vdp)

local fx, fv, fvp, fvd;

fx := -3*sin(x) + 5*cos(x);

fv := -1;

fvp := 0;

fvd := -1;

return fx + fv*vp + fvp*0 + fvd*vdp;

end proc:

# Initial conditions

a := 0: b := 10:

v0 := -5: vp0 := 3:

# Variable step-size parameters

tol := 1e-10:

h_min := 0.01:

h_max := 0.5:

h_init := Pi/8:

# Store results

X := [a]: V := [v0]: Vp := [vp0]:

h_curr := h_init:

x_curr := a:

v_curr := v0:

vp_curr := vp0:

# For history: need v at x-epsilon

get_v_delayed := proc(xx)

if xx < a then return phi(xx);

else

# Interpolate from stored solution

idx := 1;

while idx < nops(X) and X[idx] < xx do idx := idx+1; end do;

if idx = 1 then return phi(xx);

elif X[idx] = xx then return V[idx];

else

# Linear interpolation

return V[idx-1] + (V[idx]-V[idx-1])*(xx-X[idx-1])/(X[idx]-X[idx-1]);

end if;

end proc:

# Newton solver for block

solve_block := proc(x0, v0, vp0, h, omega)

local u, bet0, bet1, bet2, rho0, rho1, rho2, bet00, bet10, bet20, bet01, bet11, bet21, bet02, bet12, bet22,

rho01, rho11, rho21, rho02, rho12, rho22, F, J, V0, V1, V2, Vp0, Vp1, Vp2, tolN, iter, dv, dV;

u := omega*h;

bet0 := beta0(u); bet1 := beta1(u); bet2 := beta2(u);

rho0 := rho0(u); rho1 := rho1(u); rho2 := rho2(u);

bet00 := beta00(u); bet10 := beta10(u); bet20 := beta20(u);

bet01 := beta01(u); bet11 := beta11(u); bet21 := beta21(u);

bet02 := beta02(u); bet12 := beta12(u); bet22 := beta22(u);

rho01 := rho01(u); rho11 := rho11(u); rho21 := rho21(u);

rho02 := rho02(u); rho12 := rho12(u); rho22 := rho22(u);

# Initial guesses

V1 := v0 + h*vp0;

V2 := v0 + 2*h*vp0;

Vp1 := vp0;

Vp2 := vp0;

tolN := 1e-12;

for iter from 1 to 10 do

# Compute delayed values

vd0 := get_v_delayed(x0 - epsilon);

vd1 := get_v_delayed(x0 + h - epsilon);

vd2 := get_v_delayed(x0 + 2*h - epsilon);

vdp0 := (get_v_delayed(x0 - epsilon + 1e-8) - vd0)/1e-8;

vdp1 := (get_v_delayed(x0 + h - epsilon + 1e-8) - vd1)/1e-8;

vdp2 := (get_v_delayed(x0 + 2*h - epsilon + 1e-8) - vd2)/1e-8;

# Compute gamma and g

gam0 := f(x0, v0, vp0, vd0);

gam1 := f(x0+h, V1, Vp1, vd1);

gam2 := f(x0+2*h, V2, Vp2, vd2);

g0 := g(x0, v0, vp0, vd0, vdp0);

g1 := g(x0+h, V1, Vp1, vd1, vdp1);

g2 := g(x0+2*h, V2, Vp2, vd2, vdp2);

# Residuals

F1 := h*vp0 - (V1 - v0 + h^2*(bet00*gam0 + bet10*gam1 + bet20*gam2)

+ h^3*(rho01*g0 + rho11*g1 + rho21*g2));

F2 := h*Vp1 - (V1 - v0 + h^2*(bet01*gam0 + bet11*gam1 + bet21*gam2)

+ h^3*(rho01*g0 + rho11*g1 + rho21*g2));

F3 := h*Vp2 - (V1 - v0 + h^2*(bet02*gam0 + bet12*gam1 + bet22*gam2)

+ h^3*(rho02*g0 + rho12*g1 + rho22*g2));

F4 := V2 - (2*V1 - v0 + h^2*(bet0*gam0 + bet1*gam1 + bet2*gam2)

+ h^3*(rho0*g0 + rho1*g1 + rho2*g2));

F := Vector([F1, F2, F3, F4]);

if LinearAlgebra:-Norm(F) < tolN then break; end if;

# Approximate Jacobian (finite differences)

J := Matrix(4,4);

delta := 1e-6;

for j from 1 to 4 do

V_pert := Vector([V1, V2, Vp1, Vp2]);

V_pert[j] := V_pert[j] + delta;

V1p := V_pert[1]; V2p := V_pert[2]; Vp1p := V_pert[3]; Vp2p := V_pert[4];

gam1p := f(x0+h, V1p, Vp1p, get_v_delayed(x0+h-epsilon));

gam2p := f(x0+2*h, V2p, Vp2p, get_v_delayed(x0+2*h-epsilon));

g1p := g(x0+h, V1p, Vp1p, get_v_delayed(x0+h-epsilon),

(get_v_delayed(x0+h-epsilon+1e-8)-get_v_delayed(x0+h-epsilon))/1e-8);

g2p := g(x0+2*h, V2p, Vp2p, get_v_delayed(x0+2*h-epsilon),

(get_v_delayed(x0+2*h-epsilon+1e-8)-get_v_delayed(x0+2*h-epsilon))/1e-8);

F1p := h*vp0 - (V1p - v0 + h^2*(bet00*gam0 + bet10*gam1p + bet20*gam2p)

+ h^3*(rho01*g0 + rho11*g1p + rho21*g2p));

F2p := h*Vp1p - (V1p - v0 + h^2*(bet01*gam0 + bet11*gam1p + bet21*gam2p)

+ h^3*(rho01*g0 + rho11*g1p + rho21*g2p));

F3p := h*Vp2p - (V1p - v0 + h^2*(bet02*gam0 + bet12*gam1p + bet22*gam2p)

+ h^3*(rho02*g0 + rho12*g1p + rho22*g2p));

F4p := V2p - (2*V1p - v0 + h^2*(bet0*gam0 + bet1*gam1p + bet2*gam2p)

+ h^3*(rho0*g0 + rho1*g1p + rho2*g2p));

Fp := Vector([F1p, F2p, F3p, F4p]);

J[1..4, j] := (Fp - F)/delta;

end do;

dV := LinearAlgebra:-LinearSolve(J, -F);

V1 := V1 + dV[1]; V2 := V2 + dV[2]; Vp1 := Vp1 + dV[3]; Vp2 := Vp2 + dV[4];

end do;

return [V1, V2, Vp1, Vp2];

end proc:

# Main variable step-size loop

printf("Variable step-size integration for Example 1\n");

printf("tol = %e, h_init = %f\n", tol, h_init);

while x_curr < b - 1e-12 do

# Try current step

sol := solve_block(x_curr, v_curr, vp_curr, h_curr, omega);

V1 := sol[1]; V2 := sol[2]; Vp1 := sol[3]; Vp2 := sol[4];

# Compute with two half-steps

sol_half1 := solve_block(x_curr, v_curr, vp_curr, h_curr/2, omega);

V_mid := sol_half1[2]; Vp_mid := sol_half1[4];

sol_half2 := solve_block(x_curr + h_curr/2, V_mid, Vp_mid, h_curr/2, omega);

V2_half := sol_half2[2];

# Error estimate

err := abs(V2 - V2_half) / (2^6 - 1);

if err < tol then

# Accept step

x_next := x_curr + 2*h_curr;

X := [op(X), x_curr + h_curr, x_next];

V := [op(V), V1, V2];

Vp := [op(Vp), Vp1, Vp2];

x_curr := x_next;

v_curr := V2;

vp_curr := Vp2;

printf("x = %7.4f, h = %8.5f, err = %12.5e\n", x_curr, h_curr, err);

# Adjust step size

if err < tol/2 then

h_curr := min(2*h_curr, h_max);

end if;

else

# Reject step, reduce h

h_curr := max(h_curr/2, h_min);

printf(" Rejecting, new h = %8.5f\n", h_curr);

end if;

end do:

# Exact solution for comparison

exact := x -> 3*sin(x) - 5*cos(x);

errors := [seq(abs(V[i] - exact(X[i])), i=1..nops(X))];

# Visualization

p1 := pointplot([seq([X[i], errors[i]], i=1..nops(X))], color=red, symbol=circle,

title="Example 1: Variable Step-Size TFSB - Absolute Errors",

labels=["x", "Error"], labeldirections=[horizontal,vertical]);

p2 := plot([[x_curr, h_curr]], x=a..b, style=point, color=blue,

title="Step-size evolution", labels=["x", "h"]);

display(p1);

display(p2);

printf("\nFinal results for Example 1:\n");

printf("Number of steps: %d\n", nops(X)-1);

printf("Maximum error: %e\n", max(errors));

printf("Final step-size: %f\n", h_curr);

Unable to connect to Matlab using openlink()

Youthdoo — Fri, 08 Aug 2025 04:25:12 Z

I have Maple 2016 and Matlab 2016b installed on my Windows destop.

When I run

with(Matlab);
openlink()

in a Maple worksheet the following error window appears.

After closing the window I also see the following error message,

Error, (in Matlab:-openlink) there was a problem finding or loading matlink.dll. Refer to ?Matlab,setup for help configuring your system to work with the Matlab-link.

How to fix the connection from Maple to Matlab?

Error, invalid subscript selector

kencom1 — Mon, 23 Jun 2025 18:51:33 Z

Good day, everyone

I am trying to code HPM but it's giving me the error code "Error, invalid subscript selector
" once I increase the number of iterations above 2.

Attached below is the code.

HPM.mw

Thanks

What is wrong that the command solve does not display an answer

abdulganiy — Wed, 26 Mar 2025 14:23:17 Z

Good day, all.

Please, I am working on the following code but found out that the command solve is not displaying any result. Your assistance and suggestions would be appreciated. Thank you, and best regards.

restart;
NULL;
t := sum(a[j]*q^j, j = 0 .. 9);
H := diff(t, q);
F := diff(t, q $ 2);
p1 := simplify(eval(t, q = x)) = y[n];
p2 := simplify(eval(F, q = x)) = f[n];
p3 := simplify(eval(F, q = x + h/4)) = f[n + 1/4];
p4 := simplify(eval(F, q = x + h/2)) = f[n + 1/2];
p5 := simplify(eval(F, q = x + (3*h)/4)) = f[n + 3/4];
p6 := simplify(eval(F, q = x + h)) = f[n + 1];
p7 := simplify(eval(F, q = x + (5*h)/4)) = f[n + 5/4];
p8 := simplify(eval(F, q = x + (3*h)/2)) = f[n + 3/2];
p9 := simplify(eval(F, q = x + (7*h)/4)) = f[n + 7/4];
p10 := simplify(eval(F, q = x + 2*h)) = f[n + 2];
r := seq(a[i], i = 0 .. 9);
s := p || (1 .. 10);

solve({s}, {r});

ssystem("dir C:") result is in Spanish

minhhieuh2003 — Mon, 03 Mar 2025 05:05:11 Z

i used:
Y := ssystem("dir C:"); print(Y)
result is

[0,"\" El volumen de la unidad C es OS\n El n£mero de serie del volumen es: 54A9-09DA\n\n Directorio de C:\\Program Files\\Maple 2016"

Windows operating system English version but Maple shows Spanish result
I want result is English. Please help me

Download language_maple.mw

How can I display the symbol and the line for one line together in the legend box?

moh111 — Sat, 21 Dec 2024 11:00:47 Z

How can I display the symbol (blue solid circle) and the line (blue line) together in the legend box (( from to ))?

Download Plot1.mw

MaplePrimes - Maple 2016 Posts and Questions

How to make this code run?

Unable to connect to Matlab using openlink()

Error, invalid subscript selector

What is wrong that the command solve does not display an answer

ssystem("dir C:") result is in Spanish

How can I display the symbol and the line for one line together in the legend box?