RKMK method of solving non-damping LL equations and ferromagnet chain equations

摘要

In the paper, we introduce a kind of Lie group method to solve non-damping Landau–Lifshitz (LL) equations and the ferromagnet chain equations. The basic idea is to discretize the partial differential equation into the form dY/dt=F(t,Y), then apply the Lie group method to it. The iterative numerical algorithm can preserve the property of square conservation of the discrete equation. The algorithm has the same accuracy as the classical Runge–Kutta method. It shows that we have proposed a valid algorithm to solve ferromagnet chain equations. The method can be applied to other similar partial differential equations.