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

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 image, and the number of algebraic operations scales roughly linearly with image when image 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.