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arXiv · 0906.2888

Chebyshev Expansions for Solutions of Linear Differential Equations

Alexandre Benoit·Bruno Salvy
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Abstract

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.

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Alexandre Benoit, Bruno Salvy. 2009-06-16. Chebyshev Expansions for Solutions of Linear Differential Equations. https://doi.org/10.1145/1576702.1576709

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