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Title:Variable step-size implicit-explicit linear multistep methods for time-dependent partial differential equations
Author(s):Wang, Dong; Ruuth, Steven J.
Subject(s):Implicit-explicit (IMEX) linear multistep methods
variable step-size
Burgers’ equation
Abstract:Implicit-explicit (IMEX) linear multistep methods are popular techniques for solving partial differential equations (PDEs) with terms of different types. While fixed time-step 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, p-step 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.
Issue Date:2011
Publisher:Global Science Press
Citation Info:Wang, D. and Ruuth, S.J. 2008. Variable step-size implicit-explicit linear multistep methods for time-dependent partial differential equations, Journal of Computational Mathematics, 26(6), 838-855.
Publication Status:published or submitted for publication
Peer Reviewed:is peer reviewed
Sponsor:The work of the first and second authors was partially supported by an NSERC Canada Postgraduate Scholarship, and a grant from NSERC Canada, respectively.
Rights Information:Global Science Press holds the copyright for this technical article.
Date Available in IDEALS:2011-03-08

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