Variable stepsize diagonally implicit multistage integration methods for ordinary differential equations

Zdzislaw Jackiewicz, R. Vermiglio, M. Zennaro

Research output: Contribution to journalArticle

10 Scopus citations

Abstract

We study a class of variable stepsize general linear methods for the numerical solution of ordinary differential equations. These methods provide an alternative to the Nordsieck technique of changing the stepsize of integration. Order conditions are derived using a recent approach by Albrecht and examples of methods are given which are appropriate for stiff or nonstiff systems in sequential or parallel computing environments. A construction of variable stepsize continuous methods is also described which is facilitated by adding, in general, one extra external stage. Numerical experiments are presented which indicate that the implementation based on variable stepsize formulation is more accurate and more efficient than the implementation based on Nordsieck's technique for second-order DIMSIMs of type 1.

Original languageEnglish (US)
Pages (from-to)343-367
Number of pages25
JournalApplied Numerical Mathematics
Volume16
Issue number3
DOIs
StatePublished - Jan 1995

Keywords

  • General linear method
  • Interpolants
  • Order conditions

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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