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Numerical investigation of stochastic canonical Hamiltonian systems by high order stochastic partitioned Runge-Kutta methods

机译:高阶随机分区跑步 - kutta方法对随机典型哈密顿系统的数值研究

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In this paper, a family of arbitrary high order quadratic invariants and energy conservation parametric stochastic partitioned Runge-Kutta methods (SPRK) are constructed for stochastic canonical Hamiltonian systems where the parameters depend on some truncated random variables, step size and numerical solutions. We first apply the P-series and bi-coloured trees theory to analyze the mean-square and weak convergence order conditions of SPRK methods solving a class of single integrand stochastic differential equations. Then, a class of SPRK methods with parameters are obtained by means of W-transform and technique of truncated Wiener increments, and we prove that the methods are symplectic. Combining with order conditions, there exists a special parameter alpha* which enables convergence order in each iteration and can preserve the energy of the stochastic canonical Hamiltonian systems. Finally, the representative stochastic canonical Hamiltonian systems are selected to verify the good performance of the proposed parameter methods. (C) 2020 Elsevier B.V. All rights reserved.
机译:在本文中,为随机规范哈密顿系统构建了一系列任意高阶二次不变性和节能参数随机分区Runge-Kutta方法(Skk),其中参数取决于一些截短的随机变量,步长和数字解决方案。我们首先应用P系列和双色树木理论,分析SPRK方法的平均方形和弱聚顺序条件,求解一类单一积分随机微分方程。然后,通过W-Transform和Truncated Wiener增量的技术获得了一类具有参数的SPRK方法,并且我们证明了这些方法是辛的。结合订单条件,存在一个特殊的参数alpha *,可以在每次迭代中实现收敛顺序,并且可以保护随机规范哈密顿系统的能量。最后,选择代表随机规范哈密顿系统以验证所提出的参数方法的良好性能。 (c)2020 Elsevier B.v.保留所有权利。

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