Dears

Hope everything fine with you. I want to solve the attached problem by numarically and want to plot it but failed. Please see the attachement and correct it. I am waiting your positive respone. 

System_of_ODEs.mw

With my best regards and sincerely.

Muhammad Usman

School of Mathematical Sciences 
Peking University, Beijing, China

Hello dear! Hope you will be fine. I want to simplify the equation (4) like equation (3) in the attached file please correct it. I shall be thankful to you.

Help.mw

With my best regards and sincerely.

Muhammad Usman

School of Mathematical Sciences 
Peking University, Beijing, China

Hello!

Hope everything fine with you. Please check the following program

restart; a := 0; b := 1; Rd := .5; Ra := .2; Nc := .6; e := .2; Nr := .3; H := .9; Digits := 20;
with(LinearAlgebra);
L[0] := 1; L[1] := a+1-x;
M := 4; K := 1;
for n while n <= M do
L[n+1] := expand(-((x-2*n-a-1)*L[n]+(n+a)*L[n-1])/(n+1))
end do; printlevel := 2;
for m from 0 while m < M do
for n to 2^(K-1) do
psi[n, m] := simplify(sqrt(m+1/2.)*2^((1/2)*K)*(eval(L[m], x = 2^K*x-2*n+1)))
end do
end do;
f1 := simplify(sum(sum(c[p, q]*psi[p, q], q = 0 .. M-1), p = 1 .. 2^(K-1)));
u := collect(f1, [x], recursive);

u := -3.5276684147527874541*c[1, 3]*x^3+(4.4721359549995793928*c[1, 2]+21.166010488516724724*c[1, 3])*x^2+(-3.4641016151377545871*c[1, 1]-13.416407864998738178*c[1, 2]-34.394767043839677677*c[1, 3])*x+c[1, 0]+3.4641016151377545871*c[1, 1]+7.8262379212492639373*c[1, 2]+14.992590762699346680*c[1, 3]

f := 1+sum(A[i]*(x^(i+1)-(i+1)*x), i = 1 .. M-2)

f:=1+A[1]*(x^2-2*x)+A[2]*(x^3-3*x)

I want to equate the like powers of "x" in f ( mention as red) and u ( mention as red) for any values of M make a system of equations as

Eq[1]:=-3.5276684147527874541*c[1, 3] = A[2];

Eq[2]:=4.4721359549995793928*c[1, 2]+21.166010488516724724*c[1, 3] = A[1];

Eq[3]:=-3.4641016151377545871*c[1, 1]-13.416407864998738178*c[1, 2]-34.394767043839677677*c[1, 3] = -2*A[1]-3*A[2];

Eq[4]:=c[1, 0]+3.4641016151377545871*c[1, 1]+7.8262379212492639373*c[1, 2]+14.992590762699346680*c[1, 3] = 1;

and solve them for any values of A[1] and A[2];

Also attached the program Equate.mw

With my best regards and sincerely.

Muhammad Usman

School of Mathematical Sciences 
Peking University, Beijing, China

Hello! Hope everything fine with you. I am try to solve the three-point differential by numerical method in attached file but failed. Please see the attachement and solve my problem. I am very thankful your kind effort. Please take care.

three-point.mw

With my best regards and sincerely.

Muhammad Usman

School of Mathematical Sciences 
Peking University, Beijing, China

Dear 

Hope you will be fine. My file takes to much time to solve the system of nonlinear algebraic equations for Iterations=8. please solve my problem I will be waiting for positive response.

Error_graph.mw