Modified Homotopy Perturbation Method For Solving High-Order Integro-Differential Equation

Abstract

In this work, a new modification of homotopy perturbation method was proposed to find analytical solution of high-order integro-differential equations. The Modification process yields the Taylor series of the exact solution. Canonical polynomials are used as basis function. The assumed approximate solution was substituted into the problem considered in which the coefficients of the homotopy perturbation parameter p were compared, and then solved, resulting to a single algebraic equation. Thus, algebraic linear system of equations were obtained by equating the coefficients of various powers of the independent variables in the equation to zero,  which are then solved simultaneously using MAPLE 18 software to obtain the values of the unknown constants in the equations. The values of the unknown constants were substituted back to get the initial approximation which yield the final solution. Some examples were given to illustrate the effectiveness of the method.

Keywords: Homotopy perturbation, Integro-differential equation, Canonical polynomial, Basis function