Application of Abaoub- Shkheam Transform for Solving Linear Partial Integro – Differential Equations

Abstract

In this paper, we propose a most general form of a linear PIDE with a convolution kernel. We convert the proposed PIDE to an ordinary differential equation (ODE) using a Abaoub- Shkheam - transform (Q). Solving this ODE and applying inverse Abaoub- Shkheam an exact solution of the problem is obtained. It is observed that the Abaoub- Shkheam - transform is a simple and reliable technique for solving such equations. A variety of numerical examples are presented to show the performance and accuracy of the proposed method.