The Sinc-Galerkin method for solving boundary value problems and treatment of the boundary conditions

There are few methods practicable to numerically solve second-order singular Dirichlet-type boundary value problems with two-point boundary conditions. In this thesis we indicate that the Sinc-Galerkin method is a very powerful tool in numerically solving such problems. The method is based on approximating functions and their derivatives by using the Whittaker cardinal function. The differential equation is reduced to a system of algebraic equations via new accurate explicit approximations of the inner products without any numerical integration which is needed to solve matrix system. At the end of the thesis, the method was tested on examples with homogeneous and non-homogeneous boundary conditions.