Exponentially convergent functional-discrete method for solving Sturm-Liouville problems with potential including Dirac \delta-function

TL;DR

This paper introduces a functional-discrete method for solving Sturm-Liouville problems with potentials including L1 functions and Dirac delta-functions, achieving superexponential convergence and confirmed by numerical examples.

Contribution

The paper develops a new functional-discrete method with proven superexponential convergence for Sturm-Liouville problems involving singular potentials.

Findings

Method achieves superexponential convergence rate.

Theoretical convergence conditions are established.

Numerical examples confirm the method's effectiveness.

Abstract

In the paper we present a functional-discrete method for solving Sturm-Liouville problems with potential including function from L_{1}(0,1) and \delta-function. For both, linear and nonlinear cases the sufficient conditions providing superexponential convergence rate of the method are obtained. The question of possible software implementation of the method is discussed in detail. The theoretical results are successfully confirmed by the numerical example included in the paper.