STRONG PREDICTOR-CORRECTOR APPROXIMATION FOR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS
作者机构：School of Mathematics and Statistics Central South University Changsha 410075 China School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074 China School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074 China Department of Computer Science Oxford University Wolfson Building Parks Road Oxford OX1 3QD UK School of Mathematical Sciences Queensland University of Technology Brisbane Australia
出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)
年 卷 期：2015年第33卷第6期
页 面：587-605页
核心收录：
学科分类：07[理学]
基 金：This work is supported by National Natural Science Foundation of China (Nos. 11401594 11171125 91130003) and the New Teachers' Specialized Research Fund for the Doctoral Program from Ministry of Education of China (No. 20120162120096)
主 题：Strong predictor-corrector approximation Stochastic delay differential equa- tions Convergence Mean-square stability Numerical experiments Vectorised simulation.
摘 要：This paper presents a strong predictor-corrector method for the numerical solution of stochastic delay differential equations （SDDEs） of ItS-type. The method is proved to be mean-square convergent of order min{1/2,p} under the Lipschitz condition and the linear growth condition, where p is the exponent of HSlder 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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