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

TL;DR

This paper introduces IFOHAM, an iterative algorithm based on the first-order equation of HAM, which generalizes Picard-Lindelöf's method and demonstrates promising convergence and computational efficiency for solving nonlinear differential equations.

Contribution

The paper presents IFOHAM, a novel iterative algorithm based on the first-order HAM equation, extending Picard-Lindelöf's iteration with improved convergence control and computational simplicity.

Findings

Shows good convergence speed

Demonstrates low CPU time

Easily programmable in symbolic environments

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.