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Question: Solve nonlinear system of equations

Question:Solve nonlinear system of equations

Zeineb 530 Maple
nonlinear
March 21 2017
1

Hi

I have a nonlinear PDEs, solved using finite difference in the square

I get the following nonlinear system of equation. Is there any idea how correct the code and display the solution.

I will appreciate any help in this question.

 

restart;
n:=100;
h:=1/(n+1);

# Boundary condition

for j from 0 by 1  to n+1 do
u[0, j] = 0;
u[n+1, j] = 0;
u[j, 0] = 0;
u[j, n+1] = 0 ;
end do;
## Loop for interior point in the square
for i from 1 by 1 to  n do
for j from 1 by 1 to  n do
(u[i+1, j]-u[i, j])*(u[i+1, j]-2*u[i, j]+u[i-1, j])+h*(u[i, j+1]-2*u[i, j]+u[i, j-1]) = 0;
end do;
end do;
 

How can I solve this system of equations with unknown u[i,j], where i,j=1,..,n

 

Many thanks for any help
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