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Journal of Applied Mathematics and Computing
Erschienen in: Journal of Applied Mathematics and Computing 1-2/2016

01.10.2016 | Original Research

A new fully discrete finite difference/element approximation for fractional cable equation

verfasst von: Jincun Liu, Hong Li, Yang Liu

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2016

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Abstract

A novel fully discrete Crank–Nicolson finite element method, which is obtained by finite difference in time and finite element in space, is presented to approximate the fractional Cable equation. Compared to the L1-formula for discretizing fractional derivatives at time \(t_{n+1}\), the proposed approximate scheme is directly obtained at time \(t_{n+\frac{1}{2}}\), in which some new coefficients \((k+\frac{1}{2})^{1-\alpha }-(k-\frac{1}{2})^{1-\alpha }\) instead of \( (k+1)^{1-\alpha }-k^{1-\alpha }\) are derived. Based on the new approximate formula, the stability and error estimate are analyzed in detail and the optimal convergence rate \(O(\tau ^{\min \{1+\alpha _{1},1+\alpha _{2}\}}+h^{r+1})\) is obtained. Numerical examples in one-dimensional and two-dimensional spaces are shown to illustrate the effectiveness and feasibility of the studied algorithm.
Vorheriger Artikel Nonlocal Cauchy problems for a class of implicit impulsive fractional relaxation differential systems
Nächster Artikel The concatenated structure of cyclic codes over

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Metadaten
Titel
A new fully discrete finite difference/element approximation for fractional cable equation
verfasst von
Jincun Liu
Hong Li
Yang Liu
Publikationsdatum
01.10.2016
Verlag
Springer Berlin Heidelberg
Erschienen in
Journal of Applied Mathematics and Computing / Ausgabe 1-2/2016
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-015-0944-0

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