Error propagation of general linear methods for ordinary differential equations

J. C. Butcher, Zdzislaw Jackiewicz, W. M. Wright

Research output: Contribution to journalArticle

20 Scopus citations

Abstract

We discuss error propagation for general linear methods for ordinary differential equations up to terms of order p + 2, where p is the order of the method. These results are then applied to the estimation of local discretization errors for methods of order p and for the adjacent order p + 1. The results of numerical experiments confirm the reliability of these estimates. This research has applications in the design of robust stepsize and order changing strategies for algorithms based on general linear methods.

Original languageEnglish (US)
Pages (from-to)560-580
Number of pages21
JournalJournal of Complexity
Volume23
Issue number4-6
DOIs
StatePublished - Jan 1 2007

Keywords

  • Adaptive stepsize selection
  • Error propagation
  • General linear methods
  • Local error estimation for methods of adjacent orders
  • Nordsieck representation
  • Stability analysis

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Statistics and Probability
  • Numerical Analysis
  • Mathematics(all)
  • Control and Optimization
  • Applied Mathematics

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