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LIE, a PC program for Lie analysis of differential equations. (English) Zbl 0854.65055
Summary: LIE is a self contained PC program for the Lie analysis of ordinary or partial differential equations, either a single equation or a simultaneous set. It generates the Lie determining equations, solves them automatically, splits the solution into Lie vectors and calculates the commutators of the vectors. These steps are deterministic except for solving the Lie equations; this is done by a heuristic procedure. As there must be some cases where a heuristic procedure fails, provision is made for convenient user intervention to give help although in practice this is rarely necessary. LIE can also assist in suggesting possible special values of symbolic constants and functions that occur in the target differential equation. It is written in the symbolic mathematics language MUMATH and will run on any PC.
65L05Initial value problems for ODE (numerical methods)
34-04Machine computation, programs (ordinary differential equations)
68W30Symbolic computation and algebraic computation
34A25Analytical theory of ODE (series, transformations, transforms, operational calculus, etc.)