A new approximation for the generalized fractional derivative and its application to generalized fractional diffusion equation

被引：5
|
作者：
Ding, Qinxu [1 ]
Wong, Patricia J. Y. [1 ]
机构：
[1] Nanyang Technol Univ, Sch Elect & Elect Engn, 50 Nanyang Ave, Singapore 639798, Singapore
来源：
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2021年 / 37卷 / 01期
关键词：
diffusion; fourth order approximation; generalized fractional derivative; generalized weighted and shifted Grunwald-Letnikov difference method; numerical solution; NONPOLYNOMIAL SPLINE METHOD; FINITE-DIFFERENCE SCHEME; NUMERICAL-SOLUTIONS;
D O I：
10.1002/num.22545
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we derive a fourth order approximation for thegeneralizedfractional derivative that is characterized by a scale functionz(t)and a weight functionw(t). Combining the new approximation with compact finite difference method, we develop a numerical scheme for a generalized fractional diffusion problem. The stability and convergence of the numerical scheme are proved by the energy method, and it is shown that the temporal and spatial convergence orders are both 4. Several numerical experiments are provided to illustrate the efficiency of our scheme.
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页码：643 / 673
页数：31
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