Delay-dependent stability of predictor–corrector methods of Runge–Kutta type for stochastic delay differential equations

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 \(\theta \) $\theta$ 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.