A new class of efficient general linear methods for ordinary differential equations

M. Braś, Z. Jackiewicz

Research output: Contribution to journalArticle

Abstract

We describe the construction of a new class of efficient general linear methods of high stage order, for nonstiff and stiff differential systems. Examples of explicit methods with large regions of stability, and implicit methods which are A- and L-stable, up to the order p=4 are presented. It is confirmed by numerical experiments that all methods achieve the expected order of accuracy and no order reduction occurs for stiff systems.

Original languageEnglish (US)
Pages (from-to)282-300
Number of pages19
JournalApplied Numerical Mathematics
Volume151
DOIs
StatePublished - May 2020
Externally publishedYes

Keywords

  • Continuous extensions
  • General linear methods
  • Local discretization errors
  • Stability analysis
  • Stage order and order conditions

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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