An iterative approximation scheme for the Landau–Lifshitz–Gilbert equation

A new iterative numerical scheme for a solution of the single Landau–Lifshitz–Gilbert equation (i.e., that the magnetic field is given) is proposed. The approach uses the fixed point technique for handling the nonlinearities at each time step. The second order of convergence in the time is proved and also confirmed by an example with an exact solution.