In a recent article \cite{manimegalai2019}, Aboodh transform based homotopy perturbation method ($AT$) 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 \cite{mehdipour2010application,nofal2013analytical} for some physically relevant anharmonic oscillators such as autonomous conservative oscillator (ACO). In the present article, expansion of frequency ($\omega$) and an auxiliary parameter ($h$) are incorporated in the framework of the homotopy perturbation method (HPM) to improve the accuracy by retaining its simplicity. Laplace transform is used to make the calculation simpler. This improved HPM ($LH$) is simple but provides highly accurate results for ACO in comparison to those obtained from $AT$. The error in the values of frequency and displacement calculated using the $LH$ is found to be one or two order of magnitude less than those obtained from $AT$ for the considered parameter sets.

中文翻译：

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使用改进的微扰方法研究自主保守振荡器

在最近的一篇文章 \cite{manimegalai2019} 中，已经发现基于 Aboodh 变换的同伦扰动方法 ($AT$) 以一种简单的方式产生近似解析解，但与从一些已建立的近似方法中获得的解相比具有更好的准确性\引用{mehdipour2010application,nofal2013analytical}一些物理相关的非谐振荡器，如自主保守振荡器（ACO）。在本文中，频率的扩展（$\omega$）和辅助参数（$h$）被纳入同伦扰动方法（HPM）的框架中，以通过保持其简单性来提高准确性。拉普拉斯变换用于使计算更简单。与从 $AT$ 获得的结果相比，这种改进的 HPM ($LH$) 很简单，但为 ACO 提供了高度准确的结果。