Convolution product and differential and integro: Differential equations

Abstract

In this paper, we consider partial differential equations with convolution term. Further, by using the convolution we propose a new method to solve the partial differential equations and compare the several properties before and after the convolution. In this new method when the operator has some singularities, then we multiply the partial differential operator with continuously differential functions by using the convolution to remove the singularity. We also study the existence and uniqueness of the new equations. In order to show numerical examples, the following types of problem will be considered: where P(D) is a differential operator. For computational purpose the computer algebra package can be used to solve recurrence relations with associated boundary conditions.