数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (2): 560-578.doi: 10.1016/S0252-9602(16)30021-2

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DISCRETE GALERKIN METHOD FOR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS

P. MOKHTARY   

  1. Department of Mathematics, Faculty of Basic Sciences, Sahand University of Technology, Tabriz, Iran
  • 收稿日期:2014-12-29 修回日期:2015-05-15 出版日期:2016-04-25 发布日期:2016-04-25
  • 作者简介:P. MOKHTARY,E-mail:mokhtary.payam@gmail.com,mokhtary@sut.ac.ir

DISCRETE GALERKIN METHOD FOR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS

P. MOKHTARY   

  1. Department of Mathematics, Faculty of Basic Sciences, Sahand University of Technology, Tabriz, Iran
  • Received:2014-12-29 Revised:2015-05-15 Online:2016-04-25 Published:2016-04-25

摘要:

In this article, we develop a fully Discrete Galerkin(DG) method for solving initial value fractional integro-differential equations(FIDEs). We consider Generalized Jacobi polynomials(GJPs) with indexes corresponding to the number of homogeneous initial conditions as natural basis functions for the approximate solution. The fractional derivatives are used in the Caputo sense. The numerical solvability of algebraic system obtained from implementation of proposed method for a special case of FIDEs is investigated. We also provide a suitable convergence analysis to approximate solutions under a more general regularity assumption on the exact solution. Numerical results are presented to demonstrate the effectiveness of the proposed method.

关键词: Fractional integro-differential equation(FIDE), Discrete Galerkin(DG), Generalized Jacobi Polynomials(GJPs), Caputo derivative

Abstract:

In this article, we develop a fully Discrete Galerkin(DG) method for solving initial value fractional integro-differential equations(FIDEs). We consider Generalized Jacobi polynomials(GJPs) with indexes corresponding to the number of homogeneous initial conditions as natural basis functions for the approximate solution. The fractional derivatives are used in the Caputo sense. The numerical solvability of algebraic system obtained from implementation of proposed method for a special case of FIDEs is investigated. We also provide a suitable convergence analysis to approximate solutions under a more general regularity assumption on the exact solution. Numerical results are presented to demonstrate the effectiveness of the proposed method.

Key words: Fractional integro-differential equation(FIDE), Discrete Galerkin(DG), Generalized Jacobi Polynomials(GJPs), Caputo derivative

中图分类号: 

  • 34A08