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

In this paper we present a functional-discrete method for solving Sturm–Liouville problems with a potential that includes a function from L1(0,1)L1(0,1) and the Dirac δδ-function. For both the linear and the nonlinear case sufficient conditions for an exponential rate of convergence of the method are obtained. The question of a possible software implementation of the method is discussed in detail. The theoretical results are successfully confirmed by a numerical example.