Abel ODEs: Equivalence and Integrable Classes
数学物理
2009-10-31 v1 天体物理学
偏微分方程分析
经典分析与常微分方程
动力系统
综合数学
math.MP
摘要
A classification, according to invariant theory, of non-constant invariant Abel ODEs known as solvable and found in the literature is presented. A set of new integrable classes depending on one or no parameters, derived from the analysis of the works by Abel, Liouville and Appell, is also shown. Computer algebra routines were developed to solve ODEs members of these classes by solving their related equivalence problem. The resulting library permits a systematic solving of Abel type ODEs in the Maple symbolic computing environment.
引用
@article{arxiv.math-ph/0001037,
title = {Abel ODEs: Equivalence and Integrable Classes},
author = {E. S. Cheb-Terrab and A. D. Roche},
journal= {arXiv preprint arXiv:math-ph/0001037},
year = {2009}
}
备注
31 pages; accepted (Jan/2000) for publication in Computer Physics Communications. Related maple programs for Abel ODEs together with the ODEtools package are available at http://lie.uwaterloo.ca/odetools.htm