भौतिक गणित

The Homotopy Analysis Method for a Fourth-Order Initial Value Problems

Abstract

Massoun Y and Benzine R

In this paper, we apply the homotopy analysis method for solving the fourth-order initial value problems by reformulating them as an equivalent system of first-order differential equations. The analytical results of the differential equations have been obtained in terms of convergent series with easily computable components. Several examples are given to illustrate the efficiency and implementation of the homotopy analysis method.