Solving Partial Integro-Differential Equations Using Laplace Transform Method

• DOI: 10.5923/j.ajcam.20120203.06
• Publication Date: 2012-09-02T22:02:58Z
• Authors: Jyoti Thorwe; Sachin Bhalekar
• Keywords: 0101 mathematics; 01 natural sciences

Partialintegro-differential equations (PIDE) occur naturally in various fields of science, engineering and social sciences. In this article, 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 Laplace transform (LT). Solving this ODE and applying inverse LT an exact solution of the problem is obtained. It is observed that the LT 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.