= = Consider 1D Poisson's Equation Uzx = 1 - 2.x2, over the domain (0,1). The boundary conditions for the system are: u(

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Consider 1d Poisson S Equation Uzx 1 2 X2 Over The Domain 0 1 The Boundary Conditions For The System Are U 1 (51.55 KiB) Viewed 35 times

= = Consider 1D Poisson's Equation Uzx = 1 - 2.x2, over the domain (0,1). The boundary conditions for the system are: u(0) = 0 and u(1) = 0. Using centered difference scheme and a mesh of 128, obtain a linear system Au = f for the problem, then solve the linear system using the following methods until a relative error of 10-4 is obtained. For each method, plot the analytical/exact solution, the numerical solution and the error distribution. Also analyze the convergence rate for each method through the plot of 2-norm of error vs. number of iteration. (a) Jacobi. (b) Gauss-Seidel. (c) Over-relaxed Jacobi with w = 1.25.