Algorithmic implementation of an exact three-point difference scheme for a certain class of singular Sturm–Liouville problems

Author:

,Khomenko N. V., ,Kutniv M. V.,

Abstract

In this article, we present a new algorithmic implementation of exact three-point difference schemes for a certain class of singular Sturm–Liouville problems. We demonstrate that computing the coefficients of the exact scheme at any grid node xj requires solving two auxiliary Cauchy problems for the second-order linear ordinary differential equations: one problem on the interval [xj−1,xj] (forward) and one problem on the interval [xj,xj+1] (backward). We have also proven the coefficient stability theorem for the exact three-point difference scheme.

Publisher

Lviv Polytechnic National University

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