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2011 An Explicit Numerical Method for the Fractional Cable Equation
J. Quintana-Murillo, S. B. Yuste
Int. J. Differ. Equ. 2011(SI1): 1-12 (2011). DOI: 10.1155/2011/231920


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.


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J. Quintana-Murillo. S. B. Yuste. "An Explicit Numerical Method for the Fractional Cable Equation." Int. J. Differ. Equ. 2011 (SI1) 1 - 12, 2011.


Received: 27 April 2011; Accepted: 30 June 2011; Published: 2011
First available in Project Euclid: 26 January 2017

zbMATH: 1237.65097
MathSciNet: MR2832509
Digital Object Identifier: 10.1155/2011/231920

Rights: Copyright © 2011 Hindawi

Vol.2011 • No. SI1 • 2011
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