Exact and discretized stability of the Bagley-Torvik equation

被引：21

作者：

Cermak, Jan ^{[1
]}

Kisela, Tomas ^{[1
]}

机构：

[1] Brno Univ Technol, Inst Math, CZ-61669 Brno, Czech Republic

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2014年 / 269卷

关键词：

Fractional differential equation; Numerical solution; Stability; Asymptotic behaviour; FRACTIONAL DIFFERENTIAL-EQUATIONS; NUMERICAL-SOLUTION; SYSTEMS;

D O I：

10.1016/j.cam.2014.03.017

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The paper discusses stability and asymptotic properties of a two-term linear fractional differential equation involving the Bagley-Torvik equation as the particular case. These properties are analysed for the exact as well as numerical solutions obtained from the Griinwald-Letnikov discretization of the studied differential equation. As the main results, precise descriptions of the exact and discretized stability regions are presented, including the decay rate of the solutions. These results enable us, among others, to observe similarities and distinctions between the asymptotic behaviour of the classical and fractional damping models. (C) 2014 Elsevier B.V. All rights reserved.

引用

页码：53 / 67

页数：15

共 33 条

[1] On Riemann and Caputo fractional differences [J].