Automatic programming of recurrent power series

The integration of differential equations by recurrent power series is a cl assical method in ODE. This method is valid on very long spans of integrati on and unusually large step-sizes. However, this method is rarely used, mai nly since each problem requires a specific formulation. In this paper, we take advantage of the facilities of the modern general pu rpose algebraic manipulators to elaborate a general program that provides a s output the Fortran code with the recurrent formulas needed for integratin g any first order differential system. We present two applications, the Hen on-Heiles problem, and the van der Pol's oscillator. For the last one, we m ake numerical comparisons between the recurrent power series method and a w ell tested Runge-Kutta one. (C) 1999 IMACS/Elsevier Science B.V. All rights reserved.