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Designing an algorithm for the series solution of nth order linear ODEs with polynomial coefficients

Nikolaos Glinos
Journal / Anthology

Innovation in Mathematics: Proceedings of the Second International Mathematica Symposium
Year: 1997
Page range: 161-168

In this paper we design an algorithm using operational calculus methods and Mathematica functional programming operators. The purpose of the algorithm is the computation of power series solutions of nth order linear differential equations in the case where the coefficients and the right hand side are polynomials or generally functions having Taylor series expansions at the origin. The algorithm performs very well, particularly when the high order derivatives (n-1), (n-2), ..., in the differential equation are missing and the polynomial coefficients do not have low degree terms.

*Mathematics > Calculus and Analysis > Differential Equations