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An Explicit Numerical Method for the Fractional Cable Equation

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  • J. Quintana-Murillo
  • S. B. Yuste

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.

Suggested Citation

  • J. Quintana-Murillo & S. B. Yuste, 2011. "An Explicit Numerical Method for the Fractional Cable Equation," International Journal of Differential Equations, Hindawi, vol. 2011, pages 1-12, September.
    • Handle: RePEc:hin:jnijde:231920
    DOI: 10.1155/2011/231920
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    Cited by:

    1. Cvetićanin, Stevan M. & Zorica, Dušan & Rapaić, Milan R., 2021. "Non-local telegrapher’s equation as a transmission line model," Applied Mathematics and Computation, Elsevier, vol. 390(C).

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