Application of He’s Variational Iteration Method to Nonlinear Integro-Differential Equations

In recent years, some promising approximate analytical solutions are proposed, such as exp-function method [1], homotopy perturbation method [2 – 11], and variational iteration method (VIM) [12 – 17]. The variational iteration method is the most effective and convenient one for both weakly and strongly nonlinear equations. This method has been shown to effectively, easily, and accurately solve a large class of nonlinear problems with component converging rapidly to accurate solutions. Avudainayagam and Vani [18] considered the application of wavelet bases in solving integro-differential equations. They introduced a new four-dimensional connection coefficient and an algorithm for its computation. They tested their algorithm by solving two simple pedagogic nonlinear integro-differential equations. El-Shaled [19] and Ghasemi et al. [20 – 22] applied He’s homotopy perturbation method to integro-differential equations. Ghasemi et al. [21, 22] and Kajani et al. [23] applied the Wavelet-Galerkin method and the sine-cosine wavelet method to integrodifferential equations. Also recently, Darania and Ebadian [24] applied the differential transform method to integro-differential equations. In this paper, we propose VIM to solve the nonlinear integro-differential equations. The Volterra integrodifferential equation is given by