Numerical solutions of higher-order second kind Fredholm integro-differential equations with modified homotopy analysis method

Abstract

We present a modified Homotopy Analysis Method (MHAM) for solving higher-order nonlinear Fredholm integro-differential equations. This approach utilizes the homotopy principles but introduces two auxiliary parameters to construct a modified homotopy. The Parameters make it easier to analyze linear and strongly nonlinear problems without linearizing the problems directly. The series solution including the recurrence relations are carefully developed and presented explicitly without the need of applying any discretization. The error estimates are tabulated while the solution plots are graphically displayed. When compared with exact solutions and other traditional methods, our scheme proved reliable, efficient, and cost-effective.