An Explicit Numerical Method for the Fractional Cable Equation

J. Quintana-Murillo and S. B. Yuste

International Journal of Differential Equations, 2011, vol. 2011, 1-12

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.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijde:231920

DOI: 10.1155/2011/231920

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