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 - <p style="text-align: justify;">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.</p>