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maxima-odesolve: a collection of ODE solvers for the maxima CAS, see http://maxima.sourceforge.net/

The purpose of this package is to provide general solvers for linear and nonlinear ordinary differential equations using a systematic approach. The general solver is a wrapper for a sequence of solvers that tackle specific (but general) ODEs, but we try to limit the number specialized routines. The core of the solver is the Prelle-Singer method, which can systematically search for Liouvillian solutions of first order ODEs. This method can be extended to search for Liouvillian solutions of nth order ODE's. If no Liouvillian solution can be found, a search for common Lie point symmetries is performed.

For second order and higher order methods, first a Loewy decomposition is performed to simplify the problem.

current:

kovacic.mac Kovacic algorithm for solving second order linear ODE's with Liouvillian solutions. This algorithm is now part of maxima. This code is based on Smith (1984) and Saunders (1981) .

PS.mac The Prelle-Singer method for solving first order ODE's that have solutions that can be written as Liouvillian functions. This code is based on Shtokhamer (1988), Man (1993) and Duarte et al.

ode2_lie.mac ode2_lie is a solver for second order nonlinear ode's using lie point symmetries. The algorithm is based on the paper of Cheb-terrab and Roche, Integrating Factors for Second Order ODEs, J. Symbolic Computation 27 (1999). This method will try to find a first integral.

To add:

separable.mac A solver for separable first order ODE's that is not based on pattern matching, based on the paper of Cid

odetype.mac determines the type of first order ODE (separable, homogeneous, etc.)

genus.mac determines the genus of the equation

Lie.mac symmetry method based on paper of Kolokolnikov to solve first order ODE's

odesystem.mac solves system of linear first order ODE's

rifsimp.mac rewrite system of partial differential equations to simplified involutive form (needed for symmetry analysis)