Solve the linear system using Jacobi Method

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Reference no: EM132157518

Assignment -

Consider 1D Poisson's Equation -uxx = 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.

Verified Expert

The project contains four parts.first part is exact solution of Poisson one dimensions equation. Which was solved on different points.second part is solve the same by linear system of equation.And compare it with exact solution graphically.Then third part by Jacobi method and comparison with exact and last by Gauss seidal method.Then conclusion and reference.

Reference no: EM132157518

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