Title :
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
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;
Conference_Titel :
Computational Sciences and Optimization, 2009. CSO 2009. International Joint Conference on
Conference_Location :
Sanya, Hainan
Print_ISBN :
978-0-7695-3605-7
DOI :
10.1109/CSO.2009.215
