TY - JOUR
T1 - Strong Predictor-Corrector Approximation for Stochastic Delay Differential Equations
AU - Niu , Yuanling
AU - Zhang , Chengjian
AU - Burrage , Kevin
JO - Journal of Computational Mathematics
VL - 6
SP - 587
EP - 605
PY - 2015
DA - 2015/12
SN - 33
DO - http://doi.org/10.4208/jcm.1507-m4505
UR - https://global-sci.org/intro/article_detail/jcm/9862.html
KW - Strong predictor-corrector approximation, Stochastic delay differential equations, Convergence, Mean-square stability, Numerical experiments, Vectorised simulation.
AB - <p style="text-align: justify;">This paper presents a strong predictor-corrector method for the numerical solution of stochastic delay differential equations (SDDEs) of Itô-type. The method is proved to be mean-square convergent of order min{$1/2, \hat{p}$} under the Lipschitz condition and the linear growth condition, where $\hat{p}$ is the exponent of Hölder condition of the initial function. Stability criteria for this type of method are derived. It is shown that for certain choices of the flexible parameter $p$ the derived method can have a better stability property than more commonly used numerical methods. That is, for some $p$, the asymptotic MS-stability bound of the method will be much larger than that of the Euler-Maruyama method. Numerical results are reported confirming convergence properties and comparing stability properties of methods with different parameters $p$. Finally, the vectorised simulation is discussed and it is shown that this implementation is much more efficient.</p>