Numerical solution of singular Poisson equations using sinc approximation

Abstract In this article, we use the Sinc approximation to solve the single Poisson problem (where the first derivative or higher order does not have an exact answer on the border of the boundary). We have examined the Sinc Galerkin approximation to solve the single Poisson problem, and finally, to solve the Poisson problem, we will use the sinc collocation method and in this method, we will reach a linear system. By carefully choosing the length of the steps and the number of nodal points, we will solve this system with two methods, with the orthogonalization technique, a numerical approximation will be obtained. Its accuracy can be exponential and of order where is a transaction parameter and c are a constant independent of N. In the final part, we will give some numerical examples of single Poisson problems.