Chebyshev spectral collocation method for stochastic delay differential equations

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• 作者：Zhengwei Yin (1) (2)
  Siqing Gan (1)
  
  1. School of Mathematics and Statistics ; Central South University ; Changsha ; Hunan ; 410083 ; China
  2. School of Mathematics and Statistics ; Henan University of Science and Technology ; Luoyang ; Henan ; 410083 ; China
  
• 关键词：spectral collocation method ; stochastic delay differential equations ; Lamperti ; type transformation ; Chebyshev ; Gauss ; Lobatto nodes
• 刊名：Advances in Difference Equations
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：2015
• 期：1
• 全文大小：1,105 KB
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• 刊物主题：Difference and Functional Equations; Mathematics, general; Analysis; Functional Analysis; Ordinary Differential Equations; Partial Differential Equations;
• 出版者：Springer International Publishing
• ISSN：1687-1847

文摘

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 \(\frac{d}{dt}\) . \(D_{N}\) 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.