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Analysis on Sixth-Order Compact Approximations with Richardson Extrapolation for 2D Poisson Equation

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Document pages: 21 pages

Abstract: By using Richardson extrapolation and fourth-ordercompact finite difference scheme on different scale grids, a sixth-ordersolution is computed on the coarse grid. Other three techniques are applied toobtain a sixth-order solution on the fine grid, and thus give out three kindsof Richardson extrapolation-based sixth order compact computation methods. Bycarefully analyzing the truncation errors respectively on 2D Poisson equation,we compare the accuracy of these three sixth order methods theoretically.Numerical results for two test problems are discussed.

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