Computer Algebra Solving of First Order ODEs Using Symmetry Methods
E.S. Cheb-Terrab, L.G.S. Duarte, L.A.C.P. da Mota
TL;DR
This paper presents a set of Maple routines that automate the analytical solving of first-order ODEs using Lie symmetry methods, including symmetry detection, invariant construction, and solution verification.
Contribution
It introduces a comprehensive computer algebra toolkit for solving first-order ODEs with symmetry methods, enhancing automation and accuracy in symbolic analysis.
Findings
Automated determination of symmetry generators
Construction of invariant ODEs under symmetries
Verification of solutions using the routines
Abstract
A set of Maple V R.3/4 computer algebra routines for the analytical solving of 1st. order ODEs, using Lie group symmetry methods, is presented. The set of commands includes a 1st. order ODE-solver and routines for, among other things: the explicit determination of the coefficients of the infinitesimal symmetry generator; the construction of the most general invariant 1st. order ODE under given symmetries; the determination of the canonical coordinates of the underlying invariant group; and the testing of the returned results.
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