An adaptation of the Gear scheme for fractional derivatives - Archive ouverte HAL Access content directly
Journal Articles Computer Methods in Applied Mechanics and Engineering Year : 2006

An adaptation of the Gear scheme for fractional derivatives

Abstract

The Gear scheme is a three-level step algorithm, backward in time and second-order accurate for the approximation of classical time derivatives. In this contribution, the formal power of this scheme is proposed to approximate fractional derivative operators in the context of finite difference methods. Some numerical examples are presented and analysed in order to show the effectiveness of the present Gear scheme at the power a (G a-scheme) when compared to the classical Gru¨nwald–Letnikov approximation. In particular, for a fractional damped oscillator problem, the combined G a-Newmark scheme is shown to be second-order accurate.
Fichier principal
Vignette du fichier
GDMDO.pdf (384.56 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01516404 , version 1 (30-04-2017)

Licence

Attribution

Identifiers

Cite

Ana Cristina Galucio, Jean-François Deü, Stéphanie Mengué, François Dubois. An adaptation of the Gear scheme for fractional derivatives. Computer Methods in Applied Mechanics and Engineering, 2006, 195 (44-47), pp.6073-6085. ⟨10.1016/j.cma.2005.10.013⟩. ⟨hal-01516404⟩
120 View
382 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More