Construction of algebraically stable DIMSIMs

Giuseppe Izzo, Zdzislaw Jackiewicz

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

The class of general linear methods for ordinary differential equations combines the advantages of linear multistep methods (high efficiency) and Runge-Kutta methods (good stability properties such as A-, L-, or algebraic stability), while at the same time avoiding the disadvantages of these methods (poor stability of linear multistep methods, high cost for Runge-Kutta methods). In this paper we describe the construction of algebraically stable general linear methods based on the criteria proposed recently by Hewitt and Hill. We also introduce the new concept of ∈-algebraic stability and investigate its consequences. Examples of ∈-algebraically stable methods are given up to order p=4.

Original languageEnglish (US)
Pages (from-to)72-84
Number of pages13
JournalJournal of Computational and Applied Mathematics
Volume261
DOIs
StatePublished - 2014

Keywords

  • Algebraic stability
  • General linear methods
  • Order conditions

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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