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In this work we present and study an iterative algorithm used toasymptotically solve nonlinear differential equations. This algorithm(Iterative First Order HAM or IFOHAM) is based on the first order equation ofthe Homotopy Analysis Method, HAM. We show that IFOHAM generalizesPicard-Lindeloff's iteration algorithm. Moreover, IFOHAM shares with HAM thepossibility of ensuring convergence by adequately choosing c0, a convergencecontrol parameter. Preliminary results show that IFOHAM exhibits a very goodperformance both in aspects related to the speed of convergence and in aspectsrelated to the CPU calculation time. It should also be noted that the IFOHAM isa very low complexity algorithm easily programmable in a symbolic computingenvironment.

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