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arXiv · 1205.2226

High precision series solution of differential equations: Ordinary and regular singular point of second order ODEs

Amna Noreen·Kåre Olaussen
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Abstract

A subroutine for very-high-precision numerical solution of a class of ordinary differential equations is provided. For 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 time in advance.

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Amna Noreen, Kåre Olaussen. 2012-05-10. High precision series solution of differential equations: Ordinary and regular singular point of second order ODEs. https://doi.org/10.1016/j.cpc.2012.05.015

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