Simulating Stochastic Differential Equations with Conserved Quantities by Improved Explicit Stochastic Runge–Kutta Methods

Zhenyu Wang, Qiang Ma and Xiaohua Ding
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Zhenyu Wang: Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai 264209, China
Qiang Ma: Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai 264209, China
Xiaohua Ding: Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai 264209, China

Mathematics, 2020, vol. 8, issue 12, 1-15

Abstract: Explicit numerical methods have a great advantage in computational cost, but they usually fail to preserve the conserved quantity of original stochastic differential equations (SDEs). In order to overcome this problem, two improved versions of explicit stochastic Runge–Kutta methods are given such that the improved methods can preserve conserved quantity of the original SDEs in Stratonovich sense. In addition, in order to deal with SDEs with multiple conserved quantities, a strategy is represented so that the improved methods can preserve multiple conserved quantities. The mean-square convergence and ability to preserve conserved quantity of the proposed methods are proved. Numerical experiments are implemented to support the theoretical results.

Keywords: stochastic differential equations; explicit stochastic Runge–Kutta methods; mean-square convergence; conserved quantities (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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