arrow
Volume 12, Issue 1
Numerical Simulations of Stochastic Differential Equations with Multiple Conserved Quantities by Conservative Methods

Zhenyu Wang, Qiang Ma & Xiaohua Ding

East Asian J. Appl. Math., 12 (2022), pp. 53-71.

Published online: 2021-10

Export citation
  • 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.

  • AMS Subject Headings

65M10, 78A48

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{EAJAM-12-53, author = {Wang , ZhenyuMa , Qiang and Ding , Xiaohua}, title = {Numerical Simulations of Stochastic Differential Equations with Multiple Conserved Quantities by Conservative Methods}, journal = {East Asian Journal on Applied Mathematics}, year = {2021}, volume = {12}, number = {1}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.080321.090721}, url = {http://global-sci.org/intro/article_detail/eajam/19920.html} }
TY - JOUR T1 - Numerical Simulations of Stochastic Differential Equations with Multiple Conserved Quantities by Conservative Methods AU - Wang , Zhenyu AU - Ma , Qiang AU - Ding , Xiaohua JO - East Asian Journal on Applied Mathematics VL - 1 SP - 53 EP - 71 PY - 2021 DA - 2021/10 SN - 12 DO - http://doi.org/10.4208/eajam.080321.090721 UR - https://global-sci.org/intro/article_detail/eajam/19920.html KW - Stochastic differential equation, multiple conserved quantity, discrete gradient, projection, mean-square convergence. AB -

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.

Zhenyu Wang, Qiang Ma & Xiaohua Ding. (2021). Numerical Simulations of Stochastic Differential Equations with Multiple Conserved Quantities by Conservative Methods. East Asian Journal on Applied Mathematics. 12 (1). 53-71. doi:10.4208/eajam.080321.090721
Copy to clipboard
The citation has been copied to your clipboard