论文标题
使用改进的扰动方法研究自主保守振荡器
Study of autonomous conservative oscillator using an improved perturbation method
论文作者
论文摘要
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振荡器，例如自动保守振荡器（ACO）。在本文中，将频率（$ω$）和辅助参数（$ h $）的扩展纳入了同型扰动方法（HPM）的框架中，以通过保持其简单性来提高准确性。拉普拉斯变换用于使计算更简单。这种改进的HPM（$ LH $）很简单，但与从$ $ $获得的相比，ACO为ACO提供了高度准确的结果。发现使用$ LH $计算出的频率和位移值的误差比从$ $ at $获得的一个数量级少了一个或两个数量级。
In a recent article \cite{manimegalai2019}, Aboodh transform based homotopy perturbation method ($AT$) has been found to produce approximate analytical solutions in a simple way but with better accuracy in comparison to those obtained from some of the established approximation methods \cite{mehdipour2010application,nofal2013analytical} for some physically relevant anharmonic oscillators such as autonomous conservative oscillator (ACO). In the present article, expansion of frequency ($ω$) and an auxiliary parameter ($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.
