K. J. Hout and B. D. Welfert, “Unconditional Stability of Second-Order ADI Schemes Applied to Multi-Dimensional Diffusion Equations with Mixed Derivative Terms,” Applied Numerical Mathematics, 2008, Article in Press.

has been cited by the following article:

• 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.