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On the Behavior of Combination High-Order Compact Approximations with Preconditioned Methods in the Diffusion-Convection Equation
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Applied Mathematics·Volume 02 (2011)·Pages 1462–1468·Published 5 December 2011·DOI10.4236/am.2011.212208
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Abstract
In this paper, a family of high-order compact finite difference methods in combination preconditioned methods are used for solution of the Diffusion-Convection equation. We developed numerical methods by replacing the time and space derivatives by compact finite-difference approximations. The system of resulting nonlinear finite difference equations are solved by preconditioned Krylov subspace methods. Numerical results are given to verify the behavior of high-order compact approximations in combination preconditioned methods for stability, convergence. Also, the accuracy and efficiency of the proposed scheme are considered.
KeywordsCompact High-Order ApproximationDiffusion-Convection EquationKrylov Subspace MethodsPreconditioner
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