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Research in Applied Mathematics: Vol. 1
Research Article
Research in Applied Mathematics
Vol. 1 (2017), Article ID 101264, 16 pages
doi:10.11131/2017/101264

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

C. Ayouch1, E. H. Essoufi1, and M. Tilioua2

1Laboratoire MISI, FST Settat, Univ. Hassan I, 26000 Settat, Morocco

2M2I Laboratory, MAMCS Group, FST Errachidia, Univ. Moulay Ismaïl, P.O. Box 509, Boutalamine, 52000 Errachidia, Morocco

Received 14 November 2016; Accepted 24 February 2017

Editor: Jianlong Qiu

Copyright © 2017 C. Ayouch et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.

Research Article
Research in Applied Mathematics
Vol. 1 (2017), Article ID 101264, 16 pages
doi:10.11131/2017/101264

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

C. Ayouch1, E. H. Essoufi1, and M. Tilioua2

1Laboratoire MISI, FST Settat, Univ. Hassan I, 26000 Settat, Morocco

2M2I Laboratory, MAMCS Group, FST Errachidia, Univ. Moulay Ismaïl, P.O. Box 509, Boutalamine, 52000 Errachidia, Morocco

Received 14 November 2016; Accepted 24 February 2017

Editor: Jianlong Qiu

Copyright © 2017 C. Ayouch et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.