Symbolic Computation on Complex Polynomial Solution of Differential Equations

Jun Zhang
Department of Mathematics
The George Washington University
Washington, DC 20052, USA

Abstract

A symbolic computation scheme, based on the Lanczos tau-method, is proposed for obtaining exact polynomial solution to some perturbed differential equations with suitable boundary conditions. The automated tau-method uses symbolic Faber polynomials as the perturbation terms for arbitrary circular section of the complex plane and has advantages of avoiding rounding error and easy manipulation over the numerical counterpart. The method is illustrated by applying it to the modified Bessel function of the first kind I_{0}(z) and the quality of the approximation is discussed.

Key words and phrases: Tau-method approximation, Bessel functions, automated tau-method, symbolic approximations.


This article has been published in Journal of Symbolic Computation in October 1996.