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Three-stage semi-implicit stochastic Runge-Kutta methods for stochastic differential equations. (Chinese. English summary) Zbl 1174.65304

Summary: We discuss three-stage semi-implicit stochastic Runge-Kutta methods for Stratonovich stochastic differential equations. The mean-square stability properties of the methods are examined. The stability properties and numerical results show the effectiveness of these methods in the pathwise approximation of stochastic differential equations.

MSC:

65C30 Numerical solutions to stochastic differential and integral equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
34F05 Ordinary differential equations and systems with randomness
65L20 Stability and convergence of numerical methods for ordinary differential equations
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