...
  • 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Applied Mathematical Modelling >Weak forms of the locally transversal linearization (LTL) technique for stochastically driven nonlinear oscillators
【24h】

Weak forms of the locally transversal linearization (LTL) technique for stochastically driven nonlinear oscillators

机译：随机驱动非线性振荡器的局部横向线性化（LTL）技术的弱形式

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

We explore several weak forms of the locally transversal linearization (LTL) method for stochastically driven nonlinear oscillators. Owing to their computational expediency, weak forms are typically suited to cases wherein it suffices to compute the statistical moments of the response of such oscillators. We first consider a variation of stochastic LTL (SLTL) method [D. Roy, M.K. Dash, A novel stochastic locally transversal linearization (LTL) technique for engineering dynamical systems: strong solutions, Appl. Math. Mod. 29(10) (2005) 913-937, doi:10.1016/j.apm.2005.02.001] through weak replacements of the Gaussian stochastic integrals, appearing in the linearized solutions, by random variables with considerably simpler and discrete probability distributions. We also formalize another weak version wherein the linearized equations corresponding to a higher order SLTL schemes are arrived at by conditionally replacing nonlinear drift and multiplicative diffusion fields using backward Euler-Maruyama expansions [Nilanjan Saha, D. Roy, Higher order weak linearizations of stochastically driven nonlinear oscillators, Proc. Roy. Soc. A 463 (2083) (2007) 1827-1856, doi: 10.1098/rspa.2007.1852]. Error estimates for this weak form of SLTL are also briefly reported. Following this, we suggest a novel procedure to weakly correct the SLTL-based strong solutions, which capture the analyticity and continuity of flow of a dynamical system, using Girsanov transformation of measures. Here error in the replacement of the nonlinear drift field by a linearized one is corrected through the Radon-Niko-dym derivative following a Girsanov transformation of probability measures. Since the Radon-Nikodym derivative is computable in terms of a stochastic exponential of an SLTL solution, a remarkably high numerical accuracy is potentially achievable. Numerical illustrations are provided for a few nonlinear oscillators driven by additive and multiplicative noises.
机译：我们探索了随机驱动非线性振荡器的局部横向线性化（LTL）方法的几种弱形式。由于其计算上的便利性，弱形式通常适用于足以计算此类振荡器响应的统计矩的情况。我们首先考虑随机LTL（SLTL）方法的一种变化[D.罗伊（M.K.） Dash，一种用于工程动力学系统的新颖的随机局部横向线性化（LTL）技术：强大的解决方案，应用。数学。 Mod。 29（10）（2005）913-937，doi：10.1016 / j.apm.2005.02.001]，通过线性化解中出现的高斯随机积分的弱替换，用具有相当简单和离散概率分布的随机变量进行替换。我们还形式化了另一个弱形式，其中使用后向Euler-Maruyama展开[Nilanjan Saha，D. Roy，随机驱动的高阶弱线性化，通过有条件地替换非线性漂移和乘法扩散场，得出与高阶SLTL方案对应的线性化方程非线性振荡器，Proc。罗伊Soc。 A 463（2083）（2007）1827-1856，doi：10.1098 / rspa.2007.1852]。还简要报告了这种弱形式的SLTL的误差估计。在此之后，我们提出了一种新颖的方法来弱校正基于SLTL的强解，该方法使用Girsanov量度转换来捕获动力系统流的分析性和连续性。在此，通过对Girsanov概率度量进行转换后，通过Radon-Niko-dym导数校正了用线性化场替换非线性漂移场的误差。由于Radon-Nikodym导数可以根据SLTL解决方案的随机指数进行计算，因此潜在地可以获得非常高的数值精度。提供了一些由加性和乘性噪声驱动的非线性振荡器的数字图示。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号