Study of autonomous conservative oscillator using an improved perturbation method

Abstract

In a recent article [1], Aboodh transform based homotopy perturbation method (AT HP M ) has been found to produce approximate analytical solutions in a simple way but with better accuracy in comparison to those obtained from some of the established approximation methods [2,3] for some physically relevant anharmonic oscillators such as, autonomous conservative oscillator (ACO). In this article, expansion of frequency (ω) and an auxiliary parameter (h) are introduced in the framework of homotopy perturbation method (HPM) to improve the accuracy by retaining its simplicity. Laplace transform is used to make the calculation simpler. This improved HPM (LT HP M h) is simple but provides highly accurate results for ACO in comparison to those from AT HP M .