IFOHAM-an iterative algorithm based on the first-order equation of HAM: exploratory preliminary results

Abstract

In this work we present and study an iterative algorithm used to asymptotically solve nonlinear differential equations. This algorithm (Iterative First Order HAM or IFOHAM) is based on the first order equation of the Homotopy Analysis Method, HAM. We show that IFOHAM generalizes Picard-Lindeloff's iteration algorithm. Moreover, IFOHAM shares with HAM the possibility of ensuring convergence by adequately choosing c0, a convergence control parameter. Preliminary results show that IFOHAM exhibits a very good performance both in aspects related to the speed of convergence and in aspects related to the CPU calculation time. It should also be noted that the IFOHAM is a very low complexity algorithm easily programmable in a symbolic computing environment.