An efficient numerical algorithm for solving the two-dimensional fractional cable equation

Ming Zhu Li; Li Juan Chen; Qiang Xu; Xiao Hua Ding

doi:10.1186/s13662-018-1883-5

An efficient numerical algorithm for solving the two-dimensional fractional cable equation

Ming Zhu Li
, Li Juan Chen^*
, Qiang Xu
, Xiao Hua Ding

^*Corresponding author for this work

School of Science

Harbin Institute of Technology
Qingdao University of Technology
Shandong Normal University

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

10 Scopus citations

Abstract

In this paper, we consider an efficient numerical algorithm for solving the two-dimensional fractional cable equation. The stability and convergency of the numerical scheme are rigorously proved by the Fourier analysis. Then we find that the convergence order is O(τ2+hx4+hy4). Finally, numerical experiments are carried out to verify the accuracy and effectiveness of the new scheme.

Original language	English
Article number	424
Journal	Advances in Difference Equations
Volume	2018
Issue number	1
DOIs	https://doi.org/10.1186/s13662-018-1883-5
State	Published - 1 Dec 2018

Keywords

Convergence
Fourier analysis
Fractional cable equation
Stability

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10.1186/s13662-018-1883-5

Cite this

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title = "An efficient numerical algorithm for solving the two-dimensional fractional cable equation",

abstract = "In this paper, we consider an efficient numerical algorithm for solving the two-dimensional fractional cable equation. The stability and convergency of the numerical scheme are rigorously proved by the Fourier analysis. Then we find that the convergence order is O(τ2+hx4+hy4). Finally, numerical experiments are carried out to verify the accuracy and effectiveness of the new scheme.",

keywords = "Convergence, Fourier analysis, Fractional cable equation, Stability",

author = "Li, \{Ming Zhu\} and Chen, \{Li Juan\} and Qiang Xu and Ding, \{Xiao Hua\}",

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AU - Li, Ming Zhu

AU - Chen, Li Juan

AU - Xu, Qiang

AU - Ding, Xiao Hua

PY - 2018/12/1

Y1 - 2018/12/1

N2 - In this paper, we consider an efficient numerical algorithm for solving the two-dimensional fractional cable equation. The stability and convergency of the numerical scheme are rigorously proved by the Fourier analysis. Then we find that the convergence order is O(τ2+hx4+hy4). Finally, numerical experiments are carried out to verify the accuracy and effectiveness of the new scheme.

AB - In this paper, we consider an efficient numerical algorithm for solving the two-dimensional fractional cable equation. The stability and convergency of the numerical scheme are rigorously proved by the Fourier analysis. Then we find that the convergence order is O(τ2+hx4+hy4). Finally, numerical experiments are carried out to verify the accuracy and effectiveness of the new scheme.

KW - Convergence

KW - Fourier analysis

KW - Fractional cable equation

KW - Stability

UR - https://www.scopus.com/pages/publications/85057044039

U2 - 10.1186/s13662-018-1883-5

DO - 10.1186/s13662-018-1883-5

M3 - 文章

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SN - 1687-1839

VL - 2018

JO - Advances in Difference Equations

JF - Advances in Difference Equations

IS - 1

M1 - 424

ER -

An efficient numerical algorithm for solving the two-dimensional fractional cable equation

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Keywords

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