Computation of eigenfunctions of nonlinear boundary-value -transmission problems by developing some approximate techniques

Abstract

In this study, we investigate a boundary value problem for nonlinear Sturm-Liouville equations with additional transmission conditions at one interior singular point. Known numerical methods are intended for solving initial and boundary value problems without transmission conditions. By modifying the Adomian decomposition method and the differential transform method, we present a new numerical algorithm to compute the eigenvalues and eigenfunctions of the considered boundary-value-transmission problem. Some graphic illustrations of the approximate eigenfunctions are also presented.