Chebyshev spectral collocation method for stochastic delay differential equations

被引：7
作者：
Yin, Zhengwei [1 ,2 ]
Gan, Siqing [1 ]
机构：
[1] Cent S Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China
[2] Henan Univ Sci & Technol, Sch Math & Stat, Luoyang 410083, Henan, Peoples R China
来源：
ADVANCES IN DIFFERENCE EQUATIONS | 2015年
基金：
中国国家自然科学基金;
关键词：
spectral collocation method; stochastic delay differential equations; Lamperti-type transformation; Chebyshev-Gauss-Lobatto nodes;
D O I：
10.1186/s13662-015-0447-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The purpose of the paper is to propose the Chebyshev spectral collocation method to solve a certain type of stochastic delay differential equations. Based on a spectral collocation method, the scheme is constructed by applying the differentiation matrix D-N to approximate the differential operator d/dt. D-N is obtained by taking the derivative of the interpolation polynomial P-N(t), which is interpolated by choosing the first kind of Chebyshev-Gauss-Lobatto points. Finally, numerical experiments are reported to show the accuracy and effectiveness of the method.
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页数：12
相关论文
共 23 条
[1]  
Ali I, 2009, J COMPUT MATH, V27, P254
[2]  
BEUTER A, 1993, B MATH BIOL, V55, P525, DOI 10.1007/BF02460649
[3]   A REVIEW ON STOCHASTIC DIFFERENTIAL-EQUATIONS FOR APPLICATIONS IN HYDROLOGY [J].
BODO, BA ;
THOMPSON, ME ;
UNNY, TE .
STOCHASTIC HYDROLOGY AND HYDRAULICS, 1987, 1 (02) :81-100
[4]   Introduction to the numerical analysis of stochastic delay differential equations [J].
Buckwar, E .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2000, 125 (1-2) :297-307
[5]  
Canuto C., 2007, SCIENTIF COMPUT, DOI 10.1007/978-3-540-30726-6
[6]  
Christopher THB, 2000, LMS J COMPUT MATH, V3, P315
[7]  
Driver R.D., 1977, APPLMATH SCI, V1st ed.
[8]   Chebyshev finite difference approximation for the boundary value problems [J].
Elbarbary, EME ;
El-Kady, M .
APPLIED MATHEMATICS AND COMPUTATION, 2003, 139 (2-3) :513-523
[9]   Noise-induced transitions in human postural sway [J].
Eurich, CW ;
Milton, JG .
PHYSICAL REVIEW E, 1996, 54 (06) :6681-6684
[10]   THE SPECTRAL COLLOCATION METHOD FOR STOCHASTIC DIFFERENTIAL EQUATIONS [J].
Huang, Can ;
Zhang, Zhimin .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2013, 18 (03) :667-679
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