The Quotient Homotopy Analysis Method for Solving Nonlinear Initial Value Problems

This article proposes a novel version of the popular method from the ever-so-famous homotopy analysis methods, namely Quotient Homotopy Analysis Method or simply QHAM, in order to provide numerical solutions for nonlinear initial value problems. The basic approach of this method relies firstly on constructing a suitable homotopy equation so that its solution will be then established in the form of a quotient of two formulated power series which will, in its turn, be the basis stone of the general numerical solution for the nonlinear problems. Two numerical comparisons via two examples are performed between the exact solution and the approximate numerical solution to reveal the importance and potential role of the established method in this work.