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

• Published in: Journal of engineering mathematics Vol. 100; no. 1; pp. 95 - 106
• Main Authors: Moumni, M., Tilioua, M.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01-10-2016; Springer Nature B.V
• Subjects: Applications of Mathematics; Computational Mathematics and Numerical Analysis; Dynamics; Evolution; Ferromagnetism; Finite difference method; Inertia; Magnetization; Mathematical analysis; Mathematical and Computational Engineering; Mathematical Modeling and Industrial Mathematics; Mathematical models; Mathematics; Mathematics and Statistics; Numerical stability; Stability criteria; Theoretical and Applied Mechanics; Vectors (mathematics); 78A25; Ferromagnets; Magnetization dynamics; Finite difference; Inertial effects; 35B40; Numerical stability; 35Q60
• ISSN: 0022-0833; 1573-2703
• DOI: 10.1007/s10665-015-9836-4

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.