Iterative methods and high-order difference schemes for 2D elliptic problems with mixed derivative |
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Authors: | Michel Fournié Samir Karaa |
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Institution: | 1. Laboratiore MIP, CNRS UMR 5640, Université Paul Sabatier, 118 route de Narbonne, 31062, Toulouse Cedex 4, France 2. Department of Mathematics and Statistics, Sultan Qaboos University, Al-Khod 123, P. O. Box 36, Muscat, Sultanate of Oman
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Abstract: | We derive a fourth-order compact finite difference scheme for a two-dimensional elliptic problem with a mixed derivative and constant coefficients. We conduct experimental study on numerical solution of the problem discretized by the present compact scheme and the traditional second-order central difference scheme. We study the computed accuracy achieved by each scheme and the performance of the Gauss-Seidel iterative method, the preconditioned GMRES iterative method, and the multigrid method, for solving linear systems arising from the difference schemes. |
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