Chebyshev Expansions for Solutions of Linear Differential Equations

Alexandre Benoit (1) , Bruno Salvy (1)

1 ALGORITHMS - Algorithms

A Chebyshev expansion is a series in the basis of Chebyshev polynomials of the first kind. When such a series solves a linear differential equation, its coefficients satisfy a linear recurrence equation. We interpret this equation as the numerator of a fraction of linear recurrence operators. This interpretation lets us give a simple view of previous algorithms, analyze their complexity, and design a faster one for large orders.

Mots clés: Chebyshev series; Ore polynomials

Domaines: Calcul formel [cs.SC]

Alexandre Benoit, Bruno Salvy. Chebyshev Expansions for Solutions of Linear Differential Equations. ISSAC'09, Jul 2009, Seoul, South Korea. ⟨inria-00395716⟩