The Grunwald-Letnikov method for fractional differential equations

被引：307
作者：
Scherer, Rudolf [1 ]
Kalla, Shyam L. [2 ]
Tang, Yifa [3 ]
Huang, Jianfei [3 ]
机构：
[1] Karlsruhe Inst Technol, Inst Appl & Numer Math, D-76128 Karlsruhe, Germany
[2] Vyas Inst Higher Educ, Inst Math, Jodhpur, Rajasthan, India
[3] Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2011年 / 62卷 / 03期
关键词：
Fractional derivatives; Fractional differential equations; Grunwald-Letnikov approximation; Difference methods; Binomial coefficients; Stability; DIFFUSION-WAVE EQUATION; NUMERICAL-SOLUTION; OIL STRATA; SCHEME;
D O I：
10.1016/j.camwa.2011.03.054
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper is devoted to the numerical treatment of fractional differential equations. Based on the Grunwald-Letnikov definition of fractional derivatives, finite difference schemes for the approximation of the solution are discussed. The main properties of these explicit and implicit methods concerning the stability, the convergence and the error behavior are studied related to linear test equations. The asymptotic stability and the absolute stability of these methods are proved. Error representations and estimates for the truncation, propagation and global error are derived. Numerical experiments are given. (C) 2011 Elsevier Ltd. All rights reserved.
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页码：902 / 917
页数：16
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