Jacobi Spectral Collocation Method Based on Lagrange Interpolation Polynomials for Solving Nonlinear Fractional Integro-Differential Equations

作     者：Xingfa Yang Yin Yang Yanping Chen Jie Liu 

作者机构：State Key Laboratory of Advanced Design and Manufacturing for Vehicle BodyHunan UniversityChangsha 410082HunanChina Hunan Key Laboratory for Computation and Simulation in Science and EngineeringKey Laboratory of Intelligent Computing&Information Processing of Ministry of EducationSchool of Mathematics and Computational ScienceXiangtan UniversityXiangtan 411105HunanChina School of Mathematical SciencesSouth China Normal UniversityGuangzhou 510631GuangdongChina Center for Research on Leading Technology of Special EquipmentSchool of Mechanical and Electric EngineeringGuangzhou UniversityGuangzhou 510006GuangdongChina 

出 版 物：《Advances in Applied Mathematics and Mechanics》 (应用数学与力学进展（英文）)

年 卷 期：2018年第10卷第6期

页      面：1440-1458页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：The author would like to thank the referees for the helpful suggestions.The work was supported by NSFC Project(Nos.11671342,91430213,11671157 and 11771369) Project of Scientific Research Fund of Hunan Provincial Science and Technology Department(No.2018JJ2374) Key Project of Hunan Provincial Department of Education(No.17A210) 

主　　题：Spectral method nonlinear fractional derivative Volterra integro-differential equations Caputo derivative 

摘      要：In this paper,we study a class of nonlinear fractional integro-differential equations,the fractional derivative is described in the Caputo *** the properties of the Caputo derivative,we convert the fractional integro-differential equations into equivalent integral-differential equations of Volterra type with singular kernel,then we propose and analyze a spectral Jacobi-collocation approximation for nonlinear integro-differential equations of Volterra *** provide a rigorous error analysis for the spectral methods,which shows that both the errors of approximate solutions and the errors of approximate fractional derivatives of the solutions decay exponentially in L^(∞)-norm and weighted L^(2)-norm.