Abstract
In this paper, the author considers a difference scheme of Laudau-Lifshitz equation (LL for short) and modulus of u n j which are constantly remaining equal to 1. Using this iteration format error which is ordered to t / 2h 2 , the author comes to a conclusion based on several initial simulations. According to some conditions, the author gives the numerical solution, the examples of exact solution and the error comparisons of the solutions.
Highlights
The continuous Heisenberg spin chain has aroused considerable interest among physicists in the classical study of one-dimensional motion of ferromagnetic chain
In 1907, Weiss explained the property of the ferromagnetic bodies through a study about elements of the hypothesis
In 1928, Heisenberg explained the molecular field theory which is proffered by Weiss
Summary
The continuous Heisenberg spin chain has aroused considerable interest among physicists in the classical study of one-dimensional motion of ferromagnetic chain. The energy critical Schrodinger map is related to the Landau-Lifshitz equation for ferromagnetism, and it belongs to a class of geometric evolution equations including wave maps and the harmonic heat flow It has attracted a considerable attention in the past ten years. Some sufficient and necessary conditions from the solution with an external field converges to a certain solution without an external field were given [10] When both external field and anisotropy field are presented, there is no other paper discussed the explicit solution of the multi-dimensional Landau-Lifshitz equation until 2008. MATEC Web of Conferences ti-dimensional Landau-Lifshitz equation with an uprush external field and anisotropy field. In 2011, we presented a method to solve the Landau-Lifshitz equations with the external magnetic field and anisotropy field. We showed how those solutions can evolve with time and gave a series of explicit dynamic spherical cone symmetric solutions [13]
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