  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.

Numerical Analysis