Question: Find the solution to the Poisson equation u''(x) = x 2 (1 x) in the unit interval [0, 1] using homogeneous Dirichlet conditions on the

Find the solution to the Poisson equation u''(x) = x 2 (1 x) in the unit interval [0, 1] using homogeneous Dirichlet conditions on the two boundaries, u(0) = u(1) = 0. Use a uniform a grid of size n = 100. With the software mathlab Solve the system using (i) Jacobi, and (ii) Gauss-Seidel iterations. Plot (semilogy) the residual as a function of iteration number. Is this behavior expected and why?

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