The Grunwald-Letnikov method for fractional differential equations

被引：306

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.

引用

页码：902 / 917

页数：16

共 50 条

[1] Numerical stability of Grunwald-Letnikov method for time fractional delay differential equations
Li, Lei
Wang, Dongling
BIT NUMERICAL MATHEMATICS, 2022, 62 (03) : 995 - 1027
[2] An Improved Grunwald-Letnikov Fractional Differential Mask for Image Texture Enhancement
Garg, Vishwadeep
Singh, Kulbir
INTERNATIONAL JOURNAL OF ADVANCED COMPUTER SCIENCE AND APPLICATIONS, 2012, 3 (03) : 130 - 135
[3] An Improved Approximation of Grunwald-Letnikov Fractional Integral
AbdAlRahman, Alaa
Abdelaty, Amr
Soltan, Ahmed
Radwan, Ahmed G.
2021 10TH INTERNATIONAL CONFERENCE ON MODERN CIRCUITS AND SYSTEMS TECHNOLOGIES (MOCAST), 2021,
[4] A Study of the Grunwald-Letnikov Definition for Minimizing the Effects of Random Noise on Fractional Order Differential Equations
Chakraborty, Mithun
Maiti, Deepyaman
Konar, Amit
Janarthanan, Ramadoss
2008 4TH INTERNATIONAL CONFERENCE ON INFORMATION AND AUTOMATION FOR SUSTAINABILITY (ICIAFS), 2008, : 66 - +
[5] A continuous variant for Grunwald-Letnikov fractional derivatives
Neel, Marie-Christine
Abdennadher, Ali
Solofoniaina, Joelson
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2008, 387 (12) : 2750 - 2760
[6] A New Insight Into the Grunwald-Letnikov Discrete Fractional Calculus
Wei, Yiheng
Yin, Weidi
Zhao, Yanting
Wang, Yong
JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS, 2019, 14 (04):
[7] How to empower Grunwald-Letnikov fractional difference equations with available initial condition?
Wei, Yiheng
Cao, Jinde
Li, Chuang
Chen, Yangquan
NONLINEAR ANALYSIS-MODELLING AND CONTROL, 2022, 27 (04): : 650 - 668
[8] Convergence of the Grunwald-Letnikov scheme for time-fractional diffusion
Gorenflo, R.
Abdel-Rehim, E. A.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2007, 205 (02) : 871 - 881
[9] New Laguerre Filter Approximators to the Grunwald-Letnikov Fractional Difference
Stanislawski, Rafal
MATHEMATICAL PROBLEMS IN ENGINEERING, 2012, 2012
[10] Analytical and numerical representations for discrete Grunwald-Letnikov fractional calculus
Wei, Yiheng
Chen, YangQuan
Tse, Peter W.
Cheng, Songsong
2020 CHINESE AUTOMATION CONGRESS (CAC 2020), 2020, : 2097 - 2102

← 1 2 3 4 5 →