An ordinary differential equation solver for REDUCE

Abstract

Progress and plans for the implementation of an ordinary differential equation solver in REDUCE 3.3 are reported; the aim is to incorporate the best available methods for obtaining closed-form solutions, and to aim at the ‘best possible’ alternative when this fails. It is hoped that this will become a part of the standard REDUCE program library. Elementary capabilities have already been implemented (to the level of a first course for students), i.e methods for first order differential equations of simple types (separable, ‘homogeneous’, ‘reducible to homogeneous’, linear, exact and Bernoulli) and linear equations of any order with constant coefficients. The further methods to be used include: for first-order equations, an adaptation of Shtokhamer's [1] MACSYMA program based on the results of Prelle and Singer [2]; for higher-order linear equations, factorisation of the operator where possible, and use of methods following results of Singer [3,4] and others; and for non-linear equations, the exploitation of Lie symmetries.