Preprint Article Version 1 This version is not peer-reviewed

Solution of Volterra’s Integro-Differential Equations by Using Variational Iteration Method

Version 1 : Received: 12 May 2019 / Approved: 13 May 2019 / Online: 13 May 2019 (14:22:28 CEST)

How to cite: Mamun, A.-.A.-.; Tao, W.; Asaduzzaman, M. Solution of Volterra’s Integro-Differential Equations by Using Variational Iteration Method. Preprints 2019, 2019050164 (doi: 10.20944/preprints201905.0164.v1). Mamun, A.-.A.-.; Tao, W.; Asaduzzaman, M. Solution of Volterra’s Integro-Differential Equations by Using Variational Iteration Method. Preprints 2019, 2019050164 (doi: 10.20944/preprints201905.0164.v1).

Abstract

In this paper, we introduce some basic idea of Variational iteration method for short (VIM) to solve the Volterra’s integro-differential equations. The VIM is used to solve effectively, easily, and accurately a large class of non-linear problems with approximations which converge rapidly to accurate solutions. For linear problems, it’s exact solution can be obtained by only one iteration step due to the fact that the Lagrange multiplier can be exactly identified. It is to be noted that the Lagrange multiplier reduces the iteration on integral operator and also minimizes the computational time. The method requires no transformation or linearization of any forms. Two numerical examples are presented to show the effectiveness and efficiency of the method. Also, we compare the result with the result from Homotopy perturbation method (HPM). Finally, we investigate the absolute difference between variational iteration method and homotopy perturbation method and draw the graph of difference function by using Mathematica.

Subject Areas

Variational iteration method, Integro-differential equation, Lagrange multiplier, Homotopy perturbation method.

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