A Fourth Order Finite Difference Method for Numerical Solution of the Goursat Problem

Abstract

In this article, we consider the finite difference method for numerically solving the Goursat Problem, using uniform Cartesian grids on the square region. Numerical examples are considered to ensure accuracy of the developed method on both linear and nonlinear Goursat Problems of second order partial differential equations. The results obtained for these numerical examples validate the efficiency and expected fourth order accuracy of the method.