Integration of the stochastic underdamped harmonic oscillator by the theta-method
Integration of the stochastic underdamped harmonic oscillator by the theta-method
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用 theta 方法积分随机欠阻尼谐振子
DOI：
10.1016/j.matcom.2022.03.012
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发表时间：
2022
影响因子：
4.6
通讯作者：
T.Mitsui
中科院分区：
文献类型：
--
作者：
A.Tocino;Y.Komori;T.Mitsui
在最近的论文中，几位研究人员研究了具有加性噪声的简谐振子，结果表明，其平均总能量随着时间趋于无穷大而线性增加。与它们相反，我们考虑具有附加噪声的欠阻尼谐振子。我们的分析表明，随机欠阻尼谐振子的平均总能量仍然有界，并且渐近趋于某个值。此外，我们还给出了平均动能与平均总能量增长率之间的关系。尽管所有随机 θ 方法都保留了这种关系，因为它们具有弱二阶局部阶次，但我们表明，只有随机梯形方法才能获得由精确解给出的平均总能量及其导数的渐近值。进行数值实验来证实这些结果。
In recent papers, a simple harmonic oscillator with additive noise has been studied by several researchers, and it has been shown that its mean total energy increases linearly as time goes to infinity. In contrast to them, we consider an underdamped harmonic oscillator with additive noise. Our analysis reveals that the mean total energy of the stochastic underdamped harmonic oscillator remains bounded and it asymptotically tends to a certain value. In addition, we give a relation between the mean kinetic energy and the growth rate of the mean total energy. Whereas all stochastic θ-methods preserve this relation as they are of weak second local order, we show that only the stochastic trapezoidal method can attain the asymptotic values of the mean total energy and its derivative given by the exact solution. Numerical experiments are carried out to confirm these results.