Transformed implicit-explicit DIMSIMs with strong stability preserving explicit part

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3 Scopus citations

Abstract

For many systems of differential equations modeling problems in science and engineering, there are often natural splittings of the right hand side into two parts, one of which is non-stiff or mildly stiff, and the other part is stiff. Such systems can be efficiently treated by a class of implicit-explicit (IMEX) diagonally implicit multistage integration methods (DIMSIMs), where the stiff part is integrated by an implicit formula, and the non-stiff part is integrated by an explicit formula. We will construct methods where the explicit part has strong stability preserving (SSP) property, and the implicit part of the method is A-, or L-stable. We will also investigate stability of these methods when the implicit and explicit parts interact with each other. To be more precise, we will monitor the size of the region of absolute stability of the IMEX scheme, assuming that the implicit part of the method is A-, or L-stable. Finally, we furnish examples of SSP IMEX DIMSIMs up to the order four with good stability properties.

Original languageEnglish (US)
Pages (from-to)1343-1359
Number of pages17
JournalNumerical Algorithms
Volume81
Issue number4
DOIs
StatePublished - Aug 1 2019

Keywords

  • Construction of highly stable methods
  • DIMSIMs
  • General linear methods
  • IMEX methods
  • SSP property
  • Stability analysis

ASJC Scopus subject areas

  • Applied Mathematics

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