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Journal of Scientific Computing
Published in: Journal of Scientific Computing 3/2017

01-09-2016

Accurate Implicit–Explicit General Linear Methods with Inherent Runge–Kutta Stability

Authors: Michał Braś, Giuseppe Izzo, Zdzisław Jackiewicz

Published in: Journal of Scientific Computing | Issue 3/2017

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Abstract

We investigate implicit–explicit (IMEX) general linear methods (GLMs) with inherent Runge–Kutta stability (IRKS) for differential systems with non-stiff and stiff processes. The construction of such formulas starts with implicit GLMs with IRKS which are A- and L-stable, and then we ‘remove’ implicitness in non-stiff terms by extrapolating unknown stage derivatives by stage derivatives which are already computed by the method. Then we search for IMEX schemes with large regions of absolute stability of the ‘explicit part’ of the method assuming that the ‘implicit part’ of the scheme is \(A(\alpha )\)-stable for some \(\alpha \in (0,\pi /2]\). Examples of highly stable IMEX GLMs are provided of order \(1\le p\le 4\). Numerical examples are also given which illustrate good performance of these schemes.
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Metadata
Title
Accurate Implicit–Explicit General Linear Methods with Inherent Runge–Kutta Stability
Authors
Michał Braś
Giuseppe Izzo
Zdzisław Jackiewicz
Publication date
01-09-2016
Publisher
Springer US
Published in
Journal of Scientific Computing / Issue 3/2017
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-016-0273-y

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