Unconditional Stability for Multistep ImEx Schemes: Theory
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16m1094324.pdf
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1.77 MB
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Author(s)
Seibold, Benjamin
Shirokoff, David
Zhou, Dong
Rosales, Rodolfo
Date Issued
October 2017
Journal
SIAM Journal on Numerical Analysis
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Citation
Rosales, Rodolfo R., Benjamin Seibold, David Shirokoff, and Dong Zhou. “Unconditional Stability for Multistep ImEx Schemes: Theory.” SIAM Journal on Numerical Analysis 55, no. 5 (January 2017): 2336–2360. © 2017 Society for Industrial and Applied Mathematics.
Version
Final published version
Abstract
This paper presents a new class of high order linear ImEx (implicit-explicit) multistep schemes with large regions of unconditional stability. Unconditional stability is a desirable property of a time stepping scheme, as it allows the choice of time step solely based on accuracy considerations. Of particular interest are problems for which both the implicit and explicit parts of the ImEx splitting are stiff. Such splittings can arise, for example, in variable coefficient problems, or the incompressible Navier-Stokes equations. To characterize the new ImEx schemes, an unconditional stability region is introduced, which plays a role analogous to that of the stability region in conventional multistep methods. Moreover, computable quantities (such as a numerical range) are provided that guarantee an unconditionally stable scheme for a proposed ImEx matrix splitting. The new approach is illustrated with several examples. Coefficients of the new schemes up to fifth order are provided.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1137/16M1094324
