Exponentially convergent functional-discrete method for solving Sturm-Liouville problems with potential including Dirac δ-function
Provides a highly accurate numerical method for solving a specific class of differential equations with singular potentials, but the contribution is incremental.
The paper presents a functional-discrete method for Sturm-Liouville problems with potentials including Dirac δ-functions, achieving superexponential convergence. Numerical examples confirm the theoretical results.
In the paper we present a functional-discrete method for solving Sturm-Liouville problems with potential including function from L_{1}(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.