Year: 2015
Author: Yuanling Niu, Chengjian Zhang, Kevin Burrage
Journal of Computational Mathematics, Vol. 33 (2015), Iss. 6 : pp. 587–605
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1507-m4505
Journal of Computational Mathematics, Vol. 33 (2015), Iss. 6 : pp. 587–605
Published online: 2015-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Strong predictor-corrector approximation Stochastic delay differential equations Convergence Mean-square stability Numerical experiments Vectorised simulation.