A kind of generalized backward differentiation formulae for solving fractional differential equations

Jingjun Zhao; Xingzhou Jiang; Yang Xu

doi:10.1016/j.amc.2021.126872

A kind of generalized backward differentiation formulae for solving fractional differential equations

Jingjun Zhao
, Xingzhou Jiang
, Yang Xu^*

^*Corresponding author for this work

School of Mathematics, Harbin Institute of Technology

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

A new kind of numerical method based on generalized backward differentiation formulae is established for solving fractional differential equations. An estimate of the inverse of a class of Toeplitz matrix, which is related to the method, is given. By using the estimate, convergence and stability of the method are analyzed. It is shown that the method has high order of convergence and good stability. Some numerical experiments are also given to illustrate the effectiveness of the method.

Original language	English
Article number	126872
Journal	Applied Mathematics and Computation
Volume	419
DOIs	https://doi.org/10.1016/j.amc.2021.126872
State	Published - 15 Apr 2022
Externally published	Yes

Keywords

Convergence
Fractional ordinary differential equation
Generalized backward differentiation formulae
Stability

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10.1016/j.amc.2021.126872

Cite this

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title = "A kind of generalized backward differentiation formulae for solving fractional differential equations",

abstract = "A new kind of numerical method based on generalized backward differentiation formulae is established for solving fractional differential equations. An estimate of the inverse of a class of Toeplitz matrix, which is related to the method, is given. By using the estimate, convergence and stability of the method are analyzed. It is shown that the method has high order of convergence and good stability. Some numerical experiments are also given to illustrate the effectiveness of the method.",

keywords = "Convergence, Fractional ordinary differential equation, Generalized backward differentiation formulae, Stability",

author = "Jingjun Zhao and Xingzhou Jiang and Yang Xu",

note = "Publisher Copyright: {\textcopyright} 2021",

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T1 - A kind of generalized backward differentiation formulae for solving fractional differential equations

AU - Zhao, Jingjun

AU - Jiang, Xingzhou

AU - Xu, Yang

PY - 2022/4/15

Y1 - 2022/4/15

N2 - A new kind of numerical method based on generalized backward differentiation formulae is established for solving fractional differential equations. An estimate of the inverse of a class of Toeplitz matrix, which is related to the method, is given. By using the estimate, convergence and stability of the method are analyzed. It is shown that the method has high order of convergence and good stability. Some numerical experiments are also given to illustrate the effectiveness of the method.

AB - A new kind of numerical method based on generalized backward differentiation formulae is established for solving fractional differential equations. An estimate of the inverse of a class of Toeplitz matrix, which is related to the method, is given. By using the estimate, convergence and stability of the method are analyzed. It is shown that the method has high order of convergence and good stability. Some numerical experiments are also given to illustrate the effectiveness of the method.

KW - Convergence

KW - Fractional ordinary differential equation

KW - Generalized backward differentiation formulae

KW - Stability

UR - https://www.scopus.com/pages/publications/85121786101

U2 - 10.1016/j.amc.2021.126872

DO - 10.1016/j.amc.2021.126872

M3 - 文章

AN - SCOPUS:85121786101

SN - 0096-3003

VL - 419

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

M1 - 126872

ER -

A kind of generalized backward differentiation formulae for solving fractional differential equations

Abstract

Keywords

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