RKMK method of solving non-damping LL equations and ferromagnet chain equations. (English) Zbl 1058.65099

Summary: 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.


65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
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