On the Behavior of Combination High-Order Compact Approximations with Preconditioned Methods in the Diffusion-Convection Equation ()

Ahmad Golbabai, Mahboubeh Molavi-Arabshahi

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**DOI: **10.4236/am.2011.212208
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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.

Keywords

Compact High-Order Approximation, Diffusion-Convection Equation, Krylov Subspace Methods, Preconditioner

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A. Golbabai and M. Molavi-Arabshahi, "On the Behavior of Combination High-Order Compact Approximations with Preconditioned Methods in the Diffusion-Convection Equation," *Applied Mathematics*, Vol. 2 No. 12, 2011, pp. 1462-1468. doi: 10.4236/am.2011.212208.

Conflicts of Interest

The authors declare no conflicts of interest.

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