Abel ODEs: Equivalence and Integrable Classes

Details Abel ODEs: Equivalence and Integrable Classes Abel ODEs: Equivalence and Integrable Classes

2000-01-26

arxiv.org/abs/math-ph/0001037v1

Physics

Mathematical Physics

31 pages; accepted (Jan/2000) for publication in Computer Physics Communications. Related maple programs for Abel ODEs togethe

Scientific paper

10.1016/S0010-4655(00)00042-4

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.

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