Journal of Engineering Mathematics

, Volume 100, Issue 1, pp 95–106 | Cite as

A finite-difference scheme for a model of magnetization dynamics with inertial effects



We consider a mathematical model describing magnetization dynamics with inertial effects. The model consists of a modified form of the Landau–Lifshitz–Gilbert equation for the evolution of the magnetization vector in a rigid ferromagnet. The modification lies in the presence of an acceleration term describing inertia. A semi-implicit finite-difference scheme for the model is proposed, and a criterion of numerical stability is given. Some numerical experiments are conducted to show the performance of the scheme.


Ferromagnets Finite difference Inertial effects Magnetization dynamics Numerical stability 

Mathematics Subject Classification

78A25 35Q60 35B40 



We would like to thank the editor and referees for their constructive comments and suggestions. The research was supported by the PHC Volubilis program MA/14/301 “Elaboration et analyse de modèles asymptotiques en micro-magnétisme, magnéto-élasticité et électro-élasticité” with joint financial support from the French Ministry of Foreign Affairs and the Moroccan Ministry of Higher Education and Scientific Research.


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Université de La RochelleMIA CNRS EA 3165La RochelleFrance
  2. 2.FST Errachidia, M2I Laboratory, MAMCS GroupBoutalamineMorocco

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