# 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 language English (US) 335-353 19 Journal of Computational and Applied Mathematics 151 2 https://doi.org/10.1016/S0377-0427(02)00753-7 Published - 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

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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