Fredholm integral equations of 1st and 2nd kinds are of practical importance and have wide range of applications. The present paper, deals mainly with system of non-linear Fredholm equations of the 2nd kind. In the present paper, the homotopy perturbation technique in different version from normal version is applied. The new version of the perturbation method confirms the simplicity and efficiency of the proposed method compared with other approximate solutions; also it confirms that this method is a suitable method for solving any nonlinear Fredholm Integral Equations of 2ndKind and / or systems of nonlinear Fredholm integral equations of 2nd kind. In the present paper, a new version of the homotopy perturbation technique is applied to solve system of nonlinear Fredholm integral equations. The new version based on the idea of considering the solution as a sum of an infinite series which is very rapid convergence to the accurate solution. The results due to the present version of the homotopy perturbation technique gave promises for further developing other issues of the homotopy perturbation method. The results due to the present method are compared with Adomain decomposition method.

In this paper, using cubic non-polynomial spline method to solve the system of two nonlinear volterra integral equations of the second kind, we have used a matlab14 program to solve the system. Finally, several illustrative examples to show the effectiveness and accuracy of this method.

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In this paper we consider non-linear system of Volterra integral equations of the second kind (NSVIEK2). Fourth order block-by-block is modified and applied to solve NSVIEK2. A comparison between approximate and exact results for two numerical examples depending on the least-square error are given to show the accuracy of the results obtained by using this method. Programs are written in matlab program version 7.0.

The aim of this paper is solving system of non-linear Volterra integral equations of the second kind (NSVIEK2) numerically using Predictor-Corrector methods (P-CM). Two multistep methods (Adams-Bashforth, Adams-Moulton). Convergence and stability of the methods are proved and some examples are presented to illustrate the methods. Programs are written in matlab program version 7.0.