Unconditional stability for multistep imex schemes: Theory

Document Type

Article

Publication Date

1-1-2017

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.

Identifier

85033389368 (Scopus)

Publication Title

SIAM Journal on Numerical Analysis

External Full Text Location

https://doi.org/10.1137/16M1094324

ISSN

00361429

First Page

2336

Last Page

2360

Issue

5

Volume

55

Grant

1719693

Fund Ref

National Science Foundation

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