A Finite Difference Scheme for the Time-Fractional Landau-Lifshitz-Bloch Equation

A Finite Difference Scheme for the Time-Fractional Landau-Lifshitz-Bloch Equation

In this paper, we study a finite difference scheme for temporal discretization of the time-fractional Landau-Lifshitz-Bloch equation, such as the fractional time derivative of order α is taken in the sense of Caputo. An existence result is established for the semi-discrete problem by Schaefer's...

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Main Authors: C. Ayouch, E. H. Essoufi, M. Tilioua
Format: Article
Language:English
Published: AgiAl Publishing House 2017-04-01
Series:Research in Applied Mathematics
Online Access:http://www.agialpress.com/journals/ram/2017/101264/
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spelling doaj-9282038c77d44df4b7212879572b7d252020-11-24T21:09:29ZengAgiAl Publishing HouseResearch in Applied Mathematics2357-04822017-04-01111610.11131/2017/101264101264A Finite Difference Scheme for the Time-Fractional Landau-Lifshitz-Bloch EquationC. Ayouch0E. H. Essoufi1M. Tilioua2Laboratoire MISI, FST Settat, Univ. Hassan I, 26000 Settat, MoroccoLaboratoire MISI, FST Settat, Univ. Hassan I, 26000 Settat, MoroccoM2I Laboratory, MAMCS Group, FST Errachidia, Univ. Moulay Ismaïl, P.O. Box 509, Boutalamine, 52000 Errachidia, MoroccoIn this paper, we study a finite difference scheme for temporal discretization of the time-fractional Landau-Lifshitz-Bloch equation, such as the fractional time derivative of order α is taken in the sense of Caputo. An existence result is established for the semi-discrete problem by Schaefer's fixed point theorem. Stability and error analysis are then provided, showing that the temporal accuracy is of order 2 − α.http://www.agialpress.com/journals/ram/2017/101264/
collection DOAJ
language English
format Article
sources DOAJ
author C. Ayouch
E. H. Essoufi
M. Tilioua
spellingShingle C. Ayouch
E. H. Essoufi
M. Tilioua
A Finite Difference Scheme for the Time-Fractional Landau-Lifshitz-Bloch Equation
Research in Applied Mathematics
author_facet C. Ayouch
E. H. Essoufi
M. Tilioua
author_sort C. Ayouch
title A Finite Difference Scheme for the Time-Fractional Landau-Lifshitz-Bloch Equation
title_short A Finite Difference Scheme for the Time-Fractional Landau-Lifshitz-Bloch Equation
title_full A Finite Difference Scheme for the Time-Fractional Landau-Lifshitz-Bloch Equation
title_fullStr A Finite Difference Scheme for the Time-Fractional Landau-Lifshitz-Bloch Equation
title_full_unstemmed A Finite Difference Scheme for the Time-Fractional Landau-Lifshitz-Bloch Equation
title_sort finite difference scheme for the time-fractional landau-lifshitz-bloch equation
publisher AgiAl Publishing House
series Research in Applied Mathematics
issn 2357-0482
publishDate 2017-04-01
description In this paper, we study a finite difference scheme for temporal discretization of the time-fractional Landau-Lifshitz-Bloch equation, such as the fractional time derivative of order α is taken in the sense of Caputo. An existence result is established for the semi-discrete problem by Schaefer's fixed point theorem. Stability and error analysis are then provided, showing that the temporal accuracy is of order 2 − α.
url http://www.agialpress.com/journals/ram/2017/101264/
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AT cayouch finitedifferenceschemeforthetimefractionallandaulifshitzblochequation
AT ehessoufi finitedifferenceschemeforthetimefractionallandaulifshitzblochequation
AT mtilioua finitedifferenceschemeforthetimefractionallandaulifshitzblochequation
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