Algorithmic realization of exact three‐point difference scheme for singular Sturm–Liouville problem

Abstract

A new algorithmic realization of exact three‐point difference schemes for a class of singular Sturm–Liouville problems is presented. It is shown that to compute the coefficients of the exact scheme in an arbitrary grid node, it is necessary to solve two auxiliary initial value problems for the second order linear ordinary differential equations: one problem on the interval (forward) and one problem on the interval (backward). Finally, the coefficient stability of the exact three‐point difference scheme is proved.