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

Document Type: Research Paper

Authors

1 Department of Mathematics, Faculty of Education and Science, Taiz University, Taiz, Yemen

2 Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad-431 004 India

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.

Keywords

Main Subjects

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### History

• Receive Date: 11 February 2019
• Revise Date: 28 February 2019
• Accept Date: 28 February 2019