A nonstandard Euler scheme for y″ + g(y)y′ + f(y)y=0

H. Kojouharov, Bruno Welfert

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

We introduce a nonstandard Euler scheme for solving the differential equation y″+g(y)y′ + f(y)y=0 which has the same linear stability properties as the differential equation and is conservative when g=0. The method is based on a physically motivated reduction of the equation to a system of two first-order equations and the use of Lie group integrators. The method is demonstrated on a few examples and compared to a standard MATLAB adaptive solver.

Original languageEnglish (US)
Pages (from-to)335-353
Number of pages19
JournalJournal of Computational and Applied Mathematics
Volume151
Issue number2
DOIs
StatePublished - Feb 15 2003

Keywords

  • Conservative method
  • Euler method
  • Lie group method
  • Nonstandard finite differnce scheme
  • Splitting

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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