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Volume 9, Issue 3
High-Order Energy-Preserving Methods for Stochastic Poisson Systems

Xiuyan Li, Qiang Ma & Xiaohua Ding

DOI: 10.4208/eajam.290518.310718

East Asian J. Appl. Math., 9 (2019), pp. 465-484.

Published online: 2019-06

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  • Abstract

A family of explicit parametric stochastic Runge-Kutta methods for stochastic Poisson systems is developed. The methods are based on perturbed collocation methods with truncated random variables and are energy-preserving. Under certain conditions, the truncation does not change the convergence order. More exactly, the methods retain the mean-square convergence order of the original stochastic Runge-Kutta method. Numerical examples show the efficiency of the methods constructed.

  • Keywords

Stochastic Poisson systems, stochastic Runge-Kutta methods, energy-preserving, mean-square convergence.

  • AMS Subject Headings

60H10, 65C20, 37N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-9-465, author = {Xiuyan Li, Qiang Ma and Xiaohua Ding}, title = {High-Order Energy-Preserving Methods for Stochastic Poisson Systems}, journal = {East Asian Journal on Applied Mathematics}, year = {2019}, volume = {9}, number = {3}, pages = {465--484}, abstract = {

A family of explicit parametric stochastic Runge-Kutta methods for stochastic Poisson systems is developed. The methods are based on perturbed collocation methods with truncated random variables and are energy-preserving. Under certain conditions, the truncation does not change the convergence order. More exactly, the methods retain the mean-square convergence order of the original stochastic Runge-Kutta method. Numerical examples show the efficiency of the methods constructed.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.290518.310718}, url = {http://global-sci.org/intro/article_detail/eajam/13162.html} }
TY - JOUR T1 - High-Order Energy-Preserving Methods for Stochastic Poisson Systems AU - Xiuyan Li, Qiang Ma & Xiaohua Ding JO - East Asian Journal on Applied Mathematics VL - 3 SP - 465 EP - 484 PY - 2019 DA - 2019/06 SN - 9 DO - http://doi.org/10.4208/eajam.290518.310718 UR - https://global-sci.org/intro/article_detail/eajam/13162.html KW - Stochastic Poisson systems, stochastic Runge-Kutta methods, energy-preserving, mean-square convergence. AB -

A family of explicit parametric stochastic Runge-Kutta methods for stochastic Poisson systems is developed. The methods are based on perturbed collocation methods with truncated random variables and are energy-preserving. Under certain conditions, the truncation does not change the convergence order. More exactly, the methods retain the mean-square convergence order of the original stochastic Runge-Kutta method. Numerical examples show the efficiency of the methods constructed.

Xiuyan Li, Qiang Ma and Xiaohua Ding. (2019). High-Order Energy-Preserving Methods for Stochastic Poisson Systems. East Asian Journal on Applied Mathematics. 9 (3). 465-484. doi:10.4208/eajam.290518.310718
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