Reference no: EM132157518

Assignment -

Consider 1D Poisson's Equation -u_xx = coss(πx), over the domain (0, 1). The boundary condition for the systems are: u(0) = 0 and u(1) = 0. Using centered difference discretization and a mesh of h = 1/32, obtain a linear system Au = f for the problem, then solve the linear system using:

(1) Gaussian-Elimination with partial Pivoting

(2) Jacobi's Method

(3) Gauss-Seidel Method

For Jacobi's Method, run the iteration until a residual error of 10^-4 (in 2-norms) is obtained. For all methods, plot the analytical solution, numerical solution and the error distribution. For Jacobi's Method, compare the required number of iterations with the analysis given in the class.

Note - In the report, please include calculations of the exact solution, basic introduction of the numerical methods, information's about the linear system, and all required plots/analysis.

Please submit a printed report (max. 10 pages without counting the code and references) and list all the references you use. Attach any matlab code you use with the report.