DISCRETE GALERKIN METHOD FOR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS  

作　　者：P.MOKHTARY 

机构地区：[1]Department of Mathematics, Faculty of Basic Sciences, Sahand University of Technology

出　　处：《Acta Mathematica Scientia》2016年第2期560-578,共19页数学物理学报（B辑英文版）

摘　　要：In this article, we develop a fully Discrete Galerkin（DG） method for solving ini- tial value fractional integro-differential equations（FIDEs）. We consider Generalized Jacobi polynomials（CJPs） 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.In this article, we develop a fully Discrete Galerkin（DG） method for solving ini- tial value fractional integro-differential equations（FIDEs）. We consider Generalized Jacobi polynomials（CJPs） 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 

分 类 号：O241.8[理学—计算数学]