# Solving Nonlinear System of Mixed Volterra-fredholm Integral Equations by Using Variational Iteration Method

Volume 5, Issue 4, pp 280 - 287
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### Authors

M. Rabbani - Department of Mathematics, Sari branch, Islamic Azad university, Sari, Iran. R. Jamali - Department of Mathematics, Sari branch, Islamic Azad university, Sari, Iran.

### Abstract

In this paper for solving nonlinear system of mixed Volterra-Fredholm integral equations by using variational iteration method, we have used differentiation for converting problem to suitable form such that it can be useful for constructing a correction functional with general lagrange multiplier. The optimum of lagrange multiplier can be found by variational theorem and by choosing of restrict variations properly. By substituting of optimum lagrange multiplier in correction functional, we obtain convergent sequences of functions and by appropriate choosing initial approximation, we can get approximate of the exact solution of the problem with few iterations. Some applications of nonlinear mixed Volterra-Fredholm integral equations arise in mathematical modeling of the Spatio-temporal development of an epidemic. So nonlinear system of mixed Volterra-Fredholm integral equations is important and useful. The above method independent of small parameter in comparison with similar works such as perturbation method. Also this method does not require discretization or linearization. Accuracy of numerical results show that the method is very effective and it is better than Adomian decomposition method since it has faster convergence and it is more simple. Also this method has a closed form and avoids the round of errors for finding approximation of the exact solution. The looking forward the proposed method can be used for solving various kinds of nonlinear problems.

### Keywords

• Nonlinear system of mixed
• Integral equation
• Variational method
• Volterra-Fredholm
• lagrange multiplier

•  65R20
•  45B05
•  45D05

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