A Sinc-Galerkin technique for the numerical solution of a class of singular boundary value problems

Abstract

Singular boundary value problems have received considerable interest in the mathematical applications in different areas of science and engineering. Due to the presence of a singularity, these problems raise difficulties in obtaining their analytic or numerical solutions, and various schemes have been proposed to overcome these difficulties. However, among existing techniques, the Sinc-Galerkin and Sinc-collocation methods are well-suited for handling the singularity and have high performance on boundary value problems with unbounded domains. In this work, the Sinc-Galerkin scheme is implemented to find a numerical solution of singular two-point boundary value problems arising in various physical models. Some properties of the Sinc-Galerkin method required for our subsequent development are given and are utilized to reduce the computation of solution of singular boundary value problem (BVP) to some nonlinear systems of equations. The accuracy and reliability of the proposed method are demonstrated by five test problems arising in physiology and engineering. The results are found to be in good agreement with the numerical/exact/available solutions.