Unformatted text preview: tri-diagonal system for your direct solver. Calculate the number iterations required to iterate to convergence for the Jacobi, Gauss-Siedel, and S.O.R. methods, using either the L2, or sup-norm, of either the residual error, or the rate of change of the iterates, or both. For the S.O.R. method, plot how the number of iterations changes with the relaxation parameter, λ , over the range 0.5 < λ < 1.99. Compare the absolute error of the accuracy of the methods to the exact solution from the formula you began with. Choose any stopping criteria. For Gauss-Siedel, plot the absolute error, and the approximate error used for the stopping criteria, as a function of iteration, on a log plot. Finally, for the S.O.R. scheme, try a 4 th order discretization of 2 2 x p ∂ ∂ with one Dirichlet B.C. and one 3 rd order Neumann B.C for the polynomial function. Plot results with Tecplot....
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- Spring '07
- Numerical Analysis, Neumann, home work problem, order Neumann B.C