Modified Homotopy Perturbation Method Of Solving Asystem Of Nonlinear Integralequationsand Its Convergence Analysis

Several methods for solving nonlinear Volterra integral equations of the secondkind have been proposed by many authors, such as Adomian decomposition method,biorthogonal system method, block by block method, and Chebyshev waveletsapproach. Existence and uniqueness of the solution of nonlinear systems of Volterraintegral equations of the second kind has been discussed.Homotopy perturbation method(HPM), one of the most powerful mathematicaltool for solving nonlinear problems, was established originally by He in1998and wasfurther developed and improved by many scientists and engineers. This method is basedon the use of traditional perturbation method and homotopy technique. Using thismethod, a rapid convergent series solution can be obtained in most cases. Usually, thesolutions can be used in numerical simulation due to its high accuracy.The purpose of this paper is to obtain the approximate solutions of a system ofnonlinear Volterra integral and integro-differential equations of the second kind byusing modified homotopy perturbation method(MHPM). The convergence of thealgorithm is proved strictly and the error estimation is also given. The advantages of theMHPM are that, on the one hand, numerical results with higher accuracy can beobtained by MHPM when the traditional HPM is convergent; on the other hand, theMHPM is still convergent and can give an approximate solution with satisfactoryaccuracy when the traditional HPM is divergent.