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

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.