Review of symbolic software for the computation of Lie symmetries of differential equations. (English) Zbl 0891.65081

Hereman, W.

Euromath Bull. 1, No. 2, 45-82 (1994).

Summary: A survey of symbolic programs for the determination of Lie symmetry groups of systems of differential equations is presented. The purpose, methods and algorithms of symmetry analysis are briefly outlined. Examples illustrate the use of the software. Directions for further research and development are indicated.

MSC:

65L05	Numerical methods for initial value problems involving ordinary differential equations
68W30	Symbolic computation and algebraic computation
37C80	Symmetries, equivariant dynamical systems (MSC2010)
34C20	Transformation and reduction of ordinary differential equations and systems, normal forms
34A34	Nonlinear ordinary differential equations and systems
65Y15	Packaged methods for numerical algorithms

Keywords:

infinitesimal transformations; symbolic programs; Lie symmetry groups; systems of differential equations; algorithms; software

Software:

LIE; LIEPDE; CRACKSTAR; REDUCE; SYMMGRP.MAX; SYMMGRP; DIMSYM