DISCRETE GALERKIN METHOD FOR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS

doi:10.1016/S0252-9602(16)30021-2

摘要/Abstract

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:

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

中图分类号:

34A08

P. MOKHTARY. DISCRETE GALERKIN METHOD FOR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS[J]. 数学物理学报(英文版), 2016, 36(2): 560-578.

P. MOKHTARY. DISCRETE GALERKIN METHOD FOR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS[J]. Acta mathematica scientia,Series B, 2016, 36(2): 560-578.

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