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Journal of Scientific Computing

Erschienen in:

01.12.2014

Stability and Convergence of Modified Du Fort–Frankel Schemes for Solving Time-Fractional Subdiffusion Equations

verfasst von: Hong-lin Liao, Ya-nan Zhang, Ying Zhao, Han-sheng Shi

Erschienen in: Journal of Scientific Computing | Ausgabe 3/2014

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Abstract

A class of modified Du Fort–Frankel-type schemes is investigated for fractional subdiffusion equations in the Jumarie’s modified Riemann–Liouville form with constant, variable or distributed fractional order. New explicit difference methods are constructed by combining the \(L1\) approximation of the modified fractional derivative with the idea of Du Fort–Frankel scheme, well-known for ordinary diffusion equations. Unconditional stability of the explicit methods is established in the sense of a discrete energy norm. The proposed schemes are shown to be convergent under the time-step (consistency) restriction of the classical Du Fort–Frankel scheme. Numerical examples are included to support our theoretical results.

Vorheriger Artikel A Stabilized Nitsche Fictitious Domain Method for the Stokes Problem

Nächster Artikel A New Level-Set Model for the Representation of Non-Smooth Geometries

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Titel: Stability and Convergence of Modified Du Fort–Frankel Schemes for Solving Time-Fractional Subdiffusion Equations
verfasst von: Hong-lin Liao
Ya-nan Zhang
Ying Zhao
Han-sheng Shi
Publikationsdatum: 01.12.2014
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 3/2014
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-014-9841-1

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