Numerical Solution of Singular Poisson Problems via the Sinc–Galerkin Method

Abstract

The Galerkin method is used with sinc functions for the basis elements to approximate the solution of the Poisson problem. Particular attention is paid to singular problems (a first or higher order partial derivative of the solution is undefined on the boundary). The linear system is derived and a spectral decomposition technique of solution is used. Explicit parameter selections that enhance the performance of the method are given. The method is thoroughly tested with the numerical results presented.