Delay-dependent stability of predictor-corrector methods of Runge-Kutta type for stochastic delay differential equations. (English) Zbl 1542.65012
Summary: The delay-dependent mean square stability of stochastic delay differential equations is in the forefront the structure-preserving numerical algorithms. The sufficient and necessary conditions of mean square stability for a general class of stochastic Runge-Kutta via predictor-corrector methods (SRK-PCMs) are obtained, which perform better than existing schemes. Furthermore, by regulating factor \(\theta\) in drift term in corrector step, we could explore the optimal stable regions. Several theorems about convergence and stability are proved for SRK-PCMs. A thoroughgoing system of numerical experiments verify the theorems ans remarks.
MSC:
| 65C30 | Numerical solutions to stochastic differential and integral equations |
| 60H35 | Computational methods for stochastic equations (aspects of stochastic analysis) |
| 34K50 | Stochastic functional-differential equations |
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
Keywords:
stochastic delay differential equation; stochastic Runge-Kutta scheme; predictor-corrector methods; asymptotic mean square stabilityReferences:
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