An Explicit Numerical Method for the Fractional Cable Equation. (18th September 2011)

• Record Type: Journal Article
• Authors: Quintana-Murillo, J.; Yuste, S. B.
• Other Names: Liu Fawang Academic Editor.
• Is Part Of: International journal of differential equations. Volume 2011(2011)
• Publication Date: 2011-09-18
• Subjects: Differential equations -- Periodicals; Differential equations; Periodicals; 515.35
• DOI: 10.1155/2011/231920
• Languages: English
• ISSNs: 1687-9643

Abstract

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.