Discrete gradient methods and linear projection methods for preserving a conserved quantity of stochastic differential equations |
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Authors: | Xiuyan Li Chiping Zhang Xiaohua Ding |
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Affiliation: | 1. Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai, People's Republic of China;2. School of Mathematics and Statistics, Shandong University, Weihai, People's Republic of China;3. Department of Mathematics, Harbin Institute of Technology, Harbin, People's Republic of China |
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Abstract: | Numerical methods preserving a conserved quantity for stochastic differential equations are considered. A class of discrete gradient methods based on the skew-gradient form is constructed, and the sufficient condition of convergence order 1 in the mean-square sense is given. Then a class of linear projection methods is constructed. The relationship of the two classes of methods for preserving a conserved quantity is proved, which is, the constructed linear projection methods can be considered as a subset of the constructed discrete gradient methods. Numerical experiments verify our theory and show the efficiency of proposed numerical methods. |
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Keywords: | Stochastic differential equations conserved quantity mean-square convergence discrete gradient methods linear projection methods |
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