Integrating factors for second-order ODEs
type: Item
instance of: scholarly article
title: Integrating factors for second-order ODEs
zbMATH Open document ID: 0936.65082
author: E. S. Cheb-Terrab
author: A. D. Roche
published in: Journal of Symbolic Computation
publication date: 2000-05-03T00:00:00Z
full work available at URL: https://arxiv.org/abs/math-ph/0002025
review text: In connection with second-order ordinary differential equations (ODEs), the authors present a systematic algorithm for determining the existence of integrating factors and their explicit form, when they have the forms \(\mu (x,y), \mu(x,y')\) and \(\mu(y,y')\). The algorithm can determine the existence and explicit form of the integrating factors themselves without solving any differential equations, except for a linear ODE in one subcase of the \(\mu(x,y)\) problem. Examples of ODEs not having point symmetries are shown to be solvable using the algorithm. The scheme was implemented in Maple, in the framework of the \textsl{ODEtools} package and its ODE-solver. A comparison between this implementation and other computer algebra ODE-solvers in tackling nonlinear examples from \textit{E. Kamke's} book is shown [Differentialgleichungen. Lösungsmethoden und Lösungen. 1. Gewöhnliche Differentialgleichungen (1942; Zbl 0026.31801)].
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34A05
zbMATH DE Number: 1330689
zbMATH Keywords: second-order ordinary differential equations
zbMATH Keywords: integrating factors
zbMATH Keywords: algorithm
reviewed by: Karel Najzar
describes a project that uses: Maple
describes a project that uses: CRACK
MaRDI profile type: Publication
OpenAlex ID: W1998550908
arXiv ID: math-ph/0002025
cites work: Integrating factors and first integrals for ordinary differential equations
cites work: Q4227290
cites work: Computer algebra solving second order ODEs using symmetry methods
cites work: Q3272638
cites work: Examples of the investigation of differential equations with modularized programs
cites work: Computer algebra algorithms and routines for the computation of conservation laws and fixing of gauge in differential expressions
DOI: 10.1006/JSCO.1999.0264
description: scientific article