Usage of the Variational Iteration Technique for Solving Fredholm Integro-Differential Equations

Abstract

Integral and integro-differential equations are one of the most useful mathematical tools in both pure and applied mathematics. In this article, we present a variational iteration method for solving Fredholm integro-differential equations. This study provides an analytical approximation to determine the behavior of the solution. To show the efficiency of the present method for our problems in comparison with the exact solution we report the absolute error. From the computational viewpoint, the variational iteration method is more efficient, convenient and easy to use. The method is very powerful and efficient in nding analytical as well as numerical solutions for wide classes of linear and nonlinear Fredholm integro-differential equations. Moreover, It proves the existence and uniqueness results and convergence of the solution of Fredholm integro-differential equations. Finally, some examples are included to demonstrate the validity and applicability of the proposed technique. The convergence theorem and the numerical results establish the precision and efficiency of the proposed technique.