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High precision series solutions of differential equations: Ordinary and regular singular points of second order ODEs

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posted on 06.12.2019 by Amna Noreen, Kåre Olaussen
Abstract A subroutine for a very-high-precision numerical solution of a class of ordinary differential equations is provided. For a given evaluation point and equation parameters the memory requirement scales linearly with precision P , and the number of algebraic operations scales roughly linearly with P when P becomes sufficiently large. We discuss results from extensive tests of the code, and how one, for a given evaluation point and equation parameters, may estimate precision loss and computing ti... Title of program: seriesSolveOde1 Catalogue Id: AEMW_v1_0 Nature of problem The differential equation -s 2 (d 2 /dz 2 + (1 - ν + - ν - )/z d/dz + (ν + ν - )/z 2 )ψ(z) + 1/z Σ N n-0 v n z n ψ(z) =0, is solved numerically to very high precision. The evaluation point z and some or all of the equation parameters may be complex numbers; some or all of them may be represented exactly in terms of rational numbers. Versions of this program held in the CPC repository in Mendeley Data AEMW_v1_0; seriesSolveOde1; 10.1016/j.cpc.2012.05.015 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)

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