Computer Algebra Solving of Second Order ODEs Using Symmetry Methods

Abstract

An update of the ODEtools Maple package, for the analytical solving of 1st and 2nd order ODEs using Lie group symmetry methods, is presented. The set of routines includes an ODE-solver and user-level commands realizing most of the relevant steps of the symmetry scheme. The package also includes commands for testing the returned results, and for classifying 1st and 2nd order ODEs.

24 pages, LaTeX, Soft-package (On-Line help) and sample MapleV sessions available at: http://dft.if.uerj.br/odetools.htm or http://lie.uwaterloo.ca/odetools.htm

References in corpus (1)

• Computer Algebra Solving of First Order ODEs Using Symmetry Methods

Cited by in corpus (8)

• Abel ODEs: Equivalence and Integrable Classes
• A Method to Tackle First Order Differential Equations with Liouvillian Functions in the Solution
• Nonlocal symmetries of Riccati and Abel chains and their similarity reductions
• Dealing with Rational Second Order Ordinary Differential Equations where both Darboux and Lie Find It Difficult: The $S$-function Method
• Determining Liouvillian First Integrals for Dynamical Systems in the Plane
• Computing ODE Symmetries as Abnormal Variational Symmetries
• Finding nonlocal Lie symmetries algorithmically
• Discovering Symmetries of ODEs by Symbolic Regression