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Modified Variation of Parameters Method for Second-order Integro-differential Equations and Coupled Systems

In this paper, we apply the Modified Variation of Parameters Method (MVPM) for solving second-order integro-differential equations and coupled systems of integro-differential-equations. The proposed modification is made by the elegant coupling of He's polynomials and the Ma's variation of parameters method. The proposed MVPM is applied without any discretization, transformation or restrictive assumptions and is free from round off errors, calculation of the so-called Adomian's polynomials and the identification of Lagrange multipliers. The numerical results are very encouraging.