Numerical Simulations of Stochastic Differential Equations with Multiple Conserved Quantities by Conservative Methods
Year: 2022
Author: Zhenyu Wang, Qiang Ma, Xiaohua Ding
East Asian Journal on Applied Mathematics, Vol. 12 (2022), Iss. 1 : pp. 53–71
Abstract
The deterministic discrete gradient method for stochastic differential equations is extended to equations with multiple conserved quantities. The equations with multiple conserved quantities in the Stratonovich sense are written in the skew-gradient form, which is used in the construction of the stochastic discrete gradient method. It is shown that the stochastic discrete gradient method has the mean-square convergence order one and preserves all conserved quantities. Besides, for a given skew-gradient form, the stochastic discrete gradient method is equivalent to the stochastic projection method. Numerical examples confirm the theoretical results and show the effectiveness of the method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.080321.090721
East Asian Journal on Applied Mathematics, Vol. 12 (2022), Iss. 1 : pp. 53–71
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Stochastic differential equation multiple conserved quantity discrete gradient projection mean-square convergence.
Author Details
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Conservative Continuous-Stage Stochastic Runge–Kutta Methods for Stochastic Differential Equations
Li, Xiuyan
Wang, Zhenyu
Ma, Qiang
Ding, Xiaohua
Fractal and Fractional, Vol. 7 (2023), Iss. 1 P.83
https://doi.org/10.3390/fractalfract7010083 [Citations: 1]