Temporal convergence of extrapolated BDF-2 scheme for the Maxwell-Landau-Lifshitz equations

Abstract

The Maxwell-Landau-Lifshitz equations are used to describe certain electromagnetic phenomena and are a strongly nonlinear parabolic system. This paper focuses on the optimal error estimates of a linearized second-order BDF semi-discrete scheme for the numerical approximation of the solution to the Maxwell-Landau-Lifshitz equations. The proposed algorithm is a semi-implicit scheme by using the extrapolation technique and the implicit-explicit method to linearize the nonlinear terms. Furthermore, the second-order temporal convergence rate O(τ2) is derived, where τ is the time step size. Finally, the numerical experiment is presented to confirm the theoretical result.