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Question: System of algebraic equation solved at each time step

Question:System of algebraic equation solved at each time step

Zeineb 535 Maple 17
pde finite-difference
September 11 2023
0

Dear all 
I have a PDE, with unknown u(t,x,t) ,  zero boundary condition and initial condition given

I converted the equaiton using finite difference to get a system of algebraic equation 

The system is solved at each time step 
I think i have a problem to update the solution inside the loop. 

I hope find the problem or why the numerical solution is different to exact solution at last time 

System_finite_difference.mw

Thank you for your help 
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