TITLE:
On the Behavior of Combination High-Order Compact Approximations with Preconditioned Methods in the Diffusion-Convection Equation
AUTHORS:
Ahmad Golbabai, Mahboubeh Molavi-Arabshahi
KEYWORDS:
Compact High-Order Approximation, Diffusion-Convection Equation, Krylov Subspace Methods, Preconditioner
JOURNAL NAME:
Applied Mathematics,
Vol.2 No.12,
December
27,
2011
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.