An Implicit Finite Difference Scheme with Preconditioning for Convection Dominated Diffusion Equation

Author

Song, Lunji ; Wu, Yujiang ; Wang, Yang ; Xie, Sa

Author_Institution

Sch. of Math. & Stat., Lanzhou Univ., Lanzhou, China

Volume

2

fYear

2009

fDate

24-26 April 2009

Firstpage

641

Lastpage

644

Abstract

An implicit finite difference scheme for solving time-dependent convection dominated diffusion equations in two space variables is presented. A one-sided difference approximation is used for the convection terms and a second-order central difference approximation for the diffusion term. The implicit scheme is consistent, unconditionally stable and itpsilas L² error estimation is optimal. By preconditioning technique of incremental unknowns, the implicit scheme is an efficient one.

Keywords

approximation theory; convection; difference equations; finite difference methods; numerical stability; error estimation; implicit finite difference scheme; numerical stability; one-sided difference approximation; preconditioning technique; second-order central difference approximation; space variable; time-dependent convection dominated diffusion equation; Boundary conditions; Difference equations; Error analysis; Finite difference methods; Hydrogen; Mathematics; Numerical stability; Robust stability; Statistics; Testing; Implicit scheme; convection dominated diffusion equation; finite difference; preconditioning;

fLanguage

English

Publisher

ieee

Conference_Titel

Computational Sciences and Optimization, 2009. CSO 2009. International Joint Conference on

Conference_Location

Sanya, Hainan

Print_ISBN

978-0-7695-3605-7

Type

conf

DOI

10.1109/CSO.2009.215

Filename

5194031