Recurrence Relations for the Coefficients in Ultraspherical Series Solutions of Ordinary Differential Equations
Year: 1991
Journal of Computational Mathematics, Vol. 9 (1991), Iss. 2 : pp. 171–183
Abstract
A method is presented for obtaining recurrence relations for the coefficients in ultraspherical series of linear differential equations. This method applies Doha's method (1985) to generate polynomial approximations in terms of ultraspherical polynomials of $y(zx), -1\leq x\leq 1,z\in C,|z|\leq 1$, where y is a solution of a linear differential equation. In particular, rational approximations of $y(z)$ result if $x$ is set equal to unity. Two numerical examples are given to illustrate the application of the method to first and second order differential equations. In general, the rational approximations obtained by this method are better than the corresponding polynomial approximations, and compare favourably with Pade approximants.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1991-JCM-9390
Journal of Computational Mathematics, Vol. 9 (1991), Iss. 2 : pp. 171–183
Published online: 1991-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 13