An exponentially convergent functional-discrete method for solving Sturm–Liouville problems with a potential including the Diracδ-function

Abstract

In the paper we present a functional-discrete method for solving Sturm-Liouville problems with potential including function from L1(0, 1) and δ-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.2010 Mathematical subject classification: 65L15, 65Y15, 34D10, 34L16, 34L20.