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

H. Kojouharov; Bruno Welfert

doi:10.1016/S0377-0427(02)00753-7

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

H. Kojouharov, Bruno Welfert

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	335-353
Number of pages	19
Journal	Journal of Computational and Applied Mathematics
Volume	151
Issue number	2
DOIs	https://doi.org/10.1016/S0377-0427(02)00753-7
State	Published - 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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10.1016/S0377-0427(02)00753-7

Cite this

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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.",

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AU - Kojouharov, H.

AU - Welfert, Bruno

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Y1 - 2003/2/15

N2 - 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.

AB - 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.

KW - Conservative method

KW - Euler method

KW - Lie group method

KW - Nonstandard finite differnce scheme

KW - Splitting

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JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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