Automatic programming of recurrent power series Original Research Article

The integration of differential equations by recurrent power series is a classical method in ODE. This method is valid on very long spans of integration and unusually large step-sizes. However, this method is rarely used, mainly since each problem requires a specific formulation. In this paper, we take advantage of the facilities of the modern general purpose algebraic manipulators to elaborate a general program that provides as output the Fortran code with the recurrent formulas needed for integrating any first order differential system. We present two applications, the Hénon–Heiles problem, and the van der Polʹs oscillator. For the last one, we make numerical comparisons between the recurrent power series method and a well tested Runge–Kutta one.