VARIABLE STEP-SIZE IMPLICIT-EXPLICIT LINEAR MULTISTEP METHODS FOR TIME-DEPENDENT PARTIAL DIFFERENTIAL EQUATIONS

作     者：DongWang Steven J. Ruuth 

作者机构：Department of Civil and Environmental Engineering University of Illinois at Urbana-Champaign B231 Newmark Civil Engineering Laboratory Urbana IL 61801 USA Department of Mathematics Simon Fraser University Burnaby BC Canada V5A 1S6 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2008年第26卷第6期

页      面：838-855页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by an NSERC Canada Postgraduate Scholarship supported by a grant from NSERC Canada 

主　　题：Implicit-explicit (IMEX) linear multistep methods Variable step-size Zero-stability Burgers' equation. 

摘      要：Implicit-explicit （IMEX） linear multistep methods are popular techniques for solving partial differential equations （PDEs） with terms of different types. While fixed timestep versions of such schemes have been developed and studied, implicit-explicit schemes also naturally arise in general situations where the temporal smoothness of the solution changes. In this paper we consider easily implementable variable step-size implicit-explicit （VSIMEX） linear multistep methods for time-dependent PDEs. Families of order-p, pstep VSIMEX schemes are constructed and analyzed, where p ranges from 1 to 4. The corresponding schemes are simple to implement and have the property that they reduce to the classical IMEX schemes whenever constant time step-sizes are imposed. The methods are validated on the Burgers＇ equation. These results demonstrate that by varying the time step-size, VSIMEX methods can outperform their fixed time step counterparts while still maintaining good numerical behavior.