| Contents |
| In this talk, we treat some typical sphere-valued partial differential equations, for examples,
the Heisenberg equation and the Landau-Lifshitz equation. These equations describe the evolution of spin fields in continuum ferromagnetism and have the following properties:
(1) length preserving, (2) energy conservation or dissipation property.
We propose a finite difference scheme for these equations which inherits
the above properties and show some theoretical results on the scheme.
And we also demonstrate numerical examples in order to show the effectiveness of our scheme. |
|