Construction of IMEX methods with inherent Runge-Kutta stability

Michał Braś, Giuseppe Izzo, Zdzislaw Jackiewicz

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We describe construction of implicit-explicit (IMEX) general linear methods (GLMs) with inherent Runge-Kutta stability (IRKS) for differential systems with non-stiff and stiff processes. We will use the extrapolation approach to remove implicitness in the non-stiff terms to compute unknown stage values in terms of stage derivatives at the previous step and those already computed in the current step. Highly stable IMEX GLMs of stage order equal to the order were derived up to the order four. These methods do not suffer from order reduction phenomenon which is confirmed by numerical experiments.

Original languageEnglish (US)
Title of host publicationInternational Conference of Numerical Analysis and Applied Mathematics 2015, ICNAAM 2015
EditorsTheodore E. Simos, Theodore E. Simos, Charalambos Tsitouras, Theodore E. Simos
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735413924
DOIs
StatePublished - Jun 8 2016
EventInternational Conference of Numerical Analysis and Applied Mathematics 2015, ICNAAM 2015 - Rhodes, Greece
Duration: Sep 23 2015Sep 29 2015

Publication series

NameAIP Conference Proceedings
Volume1738
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Other

OtherInternational Conference of Numerical Analysis and Applied Mathematics 2015, ICNAAM 2015
CountryGreece
CityRhodes
Period9/23/159/29/15

Keywords

  • IMEX methods
  • construction of highly stable methods
  • general linear methods
  • inherent Runge-Kutta stability

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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