Nataliya Rossokhata

Volodymyr Makarov, Nataliya Rossokhata, Denis Dragunov

Based on the functional-discrete technique (FD-method), an algorithm for eigenvalue transmission problems with discontinuous flux and integrable potential is developed. The case of the potential as a function belonging to the functional space $L_1$ is studied for both linear and nonlinear eigenvalue problems. The sufficient conditions providing superexponential convergence rate of the method were obtained. Numerical examples are presented to support the theory. Based on the numerical examples and the convergence results, conclusion about analytical properties of eigensolutions for nonself-adjoint differential operators is made.

Volodymyr Makarov, Nataliya Rossokhata, Denis Dragunov

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.