数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (3): 673-690.doi: 10.1016/S0252-9602(14)60039-4

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CONVERGENCE ANALYSIS OF THE JACOBI SPECTRAL-COLLOCATION METHOD FOR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS

杨银, 陈艳萍*, 黄云清   

  1. Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan 411105, China; School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China; Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan 411105, China
  • 收稿日期:2012-10-04 修回日期:2013-04-12 出版日期:2014-05-20 发布日期:2014-05-20
  • 作者简介:陈艳萍,yanpingchen@scnu.edu.cn
  • 基金资助:

    The work was supported by NSFC Project (11301446, 11271145), China Postdoctoral Science Foundation Grant (2013M531789), Specialized Research Fund for the Doctoral Program of Higher Education (2011440711009), Program for Changjiang Scholars and Innovative Re-search Team in University (IRT1179), Project of Scientific Research Fund of Hunan Provincial Science and Technology Department (2013RS4057), and the Research Foundation of Hunan Provincial Education Depart-ment (13B116).

CONVERGENCE ANALYSIS OF THE JACOBI SPECTRAL-COLLOCATION METHOD FOR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS

 YANG Yin, CHEN Yan-Ping*, HUANG Yun-Qing   

  1. Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan 411105, China; School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China; Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan 411105, China
  • Received:2012-10-04 Revised:2013-04-12 Online:2014-05-20 Published:2014-05-20
  • About author:CHEN Yan-Ping,yanpingchen@scnu.edu.cn
  • Supported by:

    The work was supported by NSFC Project (11301446, 11271145), China Postdoctoral Science Foundation Grant (2013M531789), Specialized Research Fund for the Doctoral Program of Higher Education (2011440711009), Program for Changjiang Scholars and Innovative Re-search Team in University (IRT1179), Project of Scientific Research Fund of Hunan Provincial Science and Technology Department (2013RS4057), and the Research Foundation of Hunan Provincial Education Depart-ment (13B116).

摘要:

We propose and analyze a spectral Jacobi-collocation approximation for frac-tional order integro-differential equations of Volterra type. The fractional derivative is de-scribed in the Caputo sense. We provide a rigorous error analysis for the collection method, which shows that the errors of the approximate solution decay exponentially in L norm and weighted L2-norm. The numerical examples are given to illustrate the theoretical results.

关键词: Spectral Jacobi-collocation method, fractional order integro-differential equa-tions, Caputo derivative

Abstract:

We propose and analyze a spectral Jacobi-collocation approximation for frac-tional order integro-differential equations of Volterra type. The fractional derivative is de-scribed in the Caputo sense. We provide a rigorous error analysis for the collection method, which shows that the errors of the approximate solution decay exponentially in L norm and weighted L2-norm. The numerical examples are given to illustrate the theoretical results.

Key words: Spectral Jacobi-collocation method, fractional order integro-differential equa-tions, Caputo derivative

中图分类号: 

  • 65R20