English

Abel ODEs: Equivalence and Integrable Classes

Mathematical Physics 2009-10-31 v1 Astrophysics Analysis of PDEs Classical Analysis and ODEs Dynamical Systems General Mathematics math.MP

Abstract

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.

Keywords

Cite

@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}
}

Comments

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