Strong convergence of the split-step theta method for neutral stochastic delay differential equations

被引：17
作者：
Yan, Zhiping
Xiao, Aiguo [1 ]
Tang, Xiao
机构：
[1] Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China
来源：
APPLIED NUMERICAL MATHEMATICS | 2017年 / 120卷
基金：
中国国家自然科学基金;
关键词：
Neutral stochastic delay differential equation; Split-step theta method; Strong convergence; Highly nonlinear condition; BACKWARD EULER METHOD; MEAN-SQUARE CONVERGENCE; EXPONENTIAL STABILITY; NUMERICAL-SOLUTIONS; APPROXIMATION; MODEL;
D O I：
10.1016/j.apnum.2017.05.008
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Neutral stochastic delay differential equations often appear in various fields of science and engineering. The aim of this article is to investigate the strong convergence of the split step theta (SST) method for the neutral stochastic delay differential equations, where the corresponding coefficients may be highly nonlinear with respect to the delay variables. In particular, we reveal that the SST method with theta is an element of [0, 1] strongly converges to the exact solution with the order 1/2. Some numerical results are presented to confirm the obtained results. (C) 2017 IMACS. Published by Elsevier B.V. All rights reserved.
引用
收藏
页码：215 / 232
页数：18
相关论文
共 38 条
[1]   Approximations of solutions to neutral functional differential equations with nonlocal history conditions [J].
Bahuguna, D ;
Agarwal, S .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 317 (02) :583-602
[2]   Retarded differential equations [J].
Baker, CTH .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2000, 125 (1-2) :309-335
[3]   Stochastic global exponential stability for neutral-type impulsive neural networks with mixed time-delays and Markovian jumping parameters [J].
Bao, Haibo ;
Cao, Jinde .
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2011, 16 (09) :3786-3791
[4]   CONVERGENCE RATE OF EM SCHEME FOR SDDEs [J].
Bao, Jianhai ;
Yuan, Chenggui .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2013, 141 (09) :3231-3243
[5]   Strong convergence of split-step backward Euler method for stochastic differential equations with non-smooth drift [J].
Bastani, Ali Foroush ;
Tahmasebi, Mahdieh .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2012, 236 (07) :1903-1918
[6]   Split-step θ-method for stochastic delay differential equations [J].
Cao, Wanrong ;
Hao, Peng ;
Zhang, Zhongqiang .
APPLIED NUMERICAL MATHEMATICS, 2014, 76 :19-33
[7]   Convergence and stability of the split-step θ-method for stochastic differential equations [J].
Ding, Xiaohua ;
Ma, Qiang ;
Zhang, Lei .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2010, 60 (05) :1310-1321
[8]   Stability of analytical and numerical solutions of nonlinear stochastic delay differential equations [J].
Gan, Siqing ;
Xiao, Aiguo ;
Wang, Desheng .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2014, 268 :5-22
[9]  
Gan SQ, 2011, INT J NUMER ANAL MOD, V8, P201
[10]   Fixed points and exponential stability for a stochastic neutral cellular neural network [J].
Guo, Chengjun ;
O'Regan, Donal ;
Deng, Feiqi ;
Agarwal, Ravi P. .
APPLIED MATHEMATICS LETTERS, 2013, 26 (08) :849-853
1234