Sinc approximation for solving fourth-order pseudo-Poisson equations

Abstract

In this article, we will investigate the Galerkin sinc approximation to solve the single pseudo-Poisson problem and in this method we will reach a linear system. We will solve this system by carefully choosing the length of the steps and the number of nodal points and with two methods; the first method, which is the usual method, is theoretically flawed and not practical and computationally efficient. Therefore, to solve the mentioned system, we introduce the orthogonalization technique, which solves both theoretical and computational problems. Numerical approximation is obtained whose accuracy is exponential and of order where N is a transaction parameter and c is a constant independent of N. In the final part, we give some numerical examples of individual pseudo-Poisson problems to demonstrate the efficiency of the method.