The homotopy analysis method and the Lienard equation

TL;DR

This paper applies the homotopy analysis method to Lienard equations to analyze their limit cycles, demonstrating that it effectively computes amplitude and frequency in agreement with computational methods.

Contribution

The study shows that the homotopy analysis method is a useful and accurate tool for solving nonlinear differential equations like the Lienard equation.

Findings

Amplitude and frequency calculations agree with computational methods.

Homotopy analysis method effectively analyzes limit cycles.

Validates the method as a reliable tool for nonlinear differential equations.

Abstract

In this work, Lienard equations are considered. The limit cycles of these systems are studied by applying the homotopy analysis method. The amplitude and frequency obtained with this methodology are in good agreement with those calculated by computational methods. This puts in evidence that the homotopy analysis method is an useful tool to solve nonlinear differential equations.