Variable step-size implicit-explicit linear multistep methods for time-dependent partial differential equations

Wang, Dong; Ruuth, Steven J.

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https://hdl.handle.net/2142/18708 Copy

Description

Title

Variable step-size implicit-explicit linear multistep methods for time-dependent partial differential equations

Author(s)

• Wang, Dong
• Ruuth, Steven J.

Issue Date

2011

Keyword(s)

• Implicit-explicit (IMEX) linear multistep methods
• variable step-size
• zero-stability
• 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.

Publisher

Global Science Press

Type of Resource

text

Permalink

http://hdl.handle.net/2142/18708

Sponsor(s)/Grant Number(s)

The work of the first and second authors was partially supported by an NSERC Canada Postgraduate Scholarship, and a grant from NSERC Canada, respectively.

Copyright and License Information

Global Science Press holds the copyright for this technical article.

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