数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (2): 580-590.doi: 10.1016/S0252-9602(18)30767-7

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NUMERICAL SIMULATIONS FOR A VARIABLE ORDER FRACTIONAL CABLE EQUATION

A. M. NAGY1, N. H. SWEILAM2   

  1. 1. Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt;
    2. Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt
  • 收稿日期:2016-08-30 修回日期:2016-11-28 出版日期:2018-04-25 发布日期:2018-04-25
  • 作者简介:A. M. NAGY,E-mail:abdelhameed nagy@yahoo.com;N. H. SWEILAM,E-mail:nsweilam@sci.cu.edu.eg

NUMERICAL SIMULATIONS FOR A VARIABLE ORDER FRACTIONAL CABLE EQUATION

A. M. NAGY1, N. H. SWEILAM2   

  1. 1. Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt;
    2. Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt
  • Received:2016-08-30 Revised:2016-11-28 Online:2018-04-25 Published:2018-04-25

摘要:

In this article, Crank-Nicolson method is used to study the variable order fractional cable equation. The variable order fractional derivatives are described in the RiemannLiouville and the Grünwald-Letnikov sense. The stability analysis of the proposed technique is discussed. Numerical results are provided and compared with exact solutions to show the accuracy of the proposed technique.

关键词: Crank-Nicolson method, variable order fractional cable equation, stability analysis

Abstract:

In this article, Crank-Nicolson method is used to study the variable order fractional cable equation. The variable order fractional derivatives are described in the RiemannLiouville and the Grünwald-Letnikov sense. The stability analysis of the proposed technique is discussed. Numerical results are provided and compared with exact solutions to show the accuracy of the proposed technique.

Key words: Crank-Nicolson method, variable order fractional cable equation, stability analysis