Construction of highly stable implicit-explicit general linear methods

Angelamaria  Cardone; Zdzisław  Jackiewicz; Adrian  Sandu; Hong  Zhang

doi:10.3934/proc.2015.0185

Article Contents

2015, Volume 2015: 185-194. Doi: 10.3934/proc.2015.0185 open access

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Construction of highly stable implicit-explicit general linear methods

1.
Dipartimento di Matematica, Università di Salerno, I-84084 Fisciano (Sa)
2.
Department of Mathematics, Arizona State University, Tempe, Arizona 85287, and AGH University of Science and Technology, Kraków
3.
Department of Computer Science, Virginia Polytechnic Institute & State University, Blacksburg, Virginia 24061
4.
Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL 60439

Received: August 31, 2014

Revised: December 31, 2014

Published: October 2015

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Abstract

This paper deals with the numerical solution of systems of differential equations with a stiff part and a non-stiff one, typically arising from the semi-discretization of certain partial differential equations models. It is illustrated the construction and analysis of highly stable and high-stage order implicit-explicit (IMEX) methods based on diagonally implicit multistage integration methods (DIMSIMs), a subclass of general linear methods (GLMs). Some examples of methods with optimal stability properties are given. Finally numerical experiments confirm the theoretical expectations.

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Mathematics Subject Classification: Primary: 65L05; Secondary: 65L20.

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References

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