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

H. Kojouharov, Bruno Welfert

Research output: Contribution to journalArticle

6 Citations (Scopus)

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

Fingerprint

Euler Scheme
Differential equations
Differential equation
Lie groups
Linear Stability
MATLAB
First-order
Standards

Keywords

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

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

Cite this

A nonstandard Euler scheme for y″ + g(y)y′ + f(y)y=0. / Kojouharov, H.; Welfert, Bruno.

In: Journal of Computational and Applied Mathematics, Vol. 151, No. 2, 15.02.2003, p. 335-353.

Research output: Contribution to journalArticle

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