## International Journal of Differential Equations

- Int. J. Differ. Equ.
- Volume 2011, Special Issue (2011), Article ID 231920, 12 pages.

### An Explicit Numerical Method for the Fractional Cable Equation

J. Quintana-Murillo and S. B. Yuste

**Full-text: Open access**

#### Abstract

An explicit numerical method to solve a fractional cable equation which involves two temporal Riemann-Liouville derivatives is studied. The numerical difference scheme is obtained by approximating the first-order derivative by a forward difference formula, the Riemann-Liouville derivatives by the Grünwald-Letnikov formula, and the spatial derivative by a three-point centered formula. The accuracy, stability, and convergence of the method are considered. The stability analysis is carried out by means of a kind of von Neumann method adapted to fractional equations. The convergence analysis is accomplished with a similar procedure. The von-Neumann stability analysis predicted very accurately the conditions under which the present explicit method is stable. This was thoroughly checked by means of extensive numerical integrations.

#### Article information

**Source**

Int. J. Differ. Equ., Volume 2011, Special Issue (2011), Article ID 231920, 12 pages.

**Dates**

Received: 27 April 2011

Accepted: 30 June 2011

First available in Project Euclid: 26 January 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.ijde/1485399984

**Digital Object Identifier**

doi:10.1155/2011/231920

**Mathematical Reviews number (MathSciNet)**

MR2832509

**Zentralblatt MATH identifier**

1237.65097

#### Citation

Quintana-Murillo, J.; Yuste, S. B. An Explicit Numerical Method for the Fractional Cable Equation. Int. J. Differ. Equ. 2011, Special Issue (2011), Article ID 231920, 12 pages. doi:10.1155/2011/231920. https://projecteuclid.org/euclid.ijde/1485399984

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