We construct new higher-order implicit-explicit (IMEX) schemes using the generalized scalar auxiliary variable (GSAV) approach for the Landau-Lifshitz equation. These schemes are linear, length preserving and only require solving one elliptic equation with constant coefficients at each time step. We show that numerical solutions of these schemes are uniformly bounded without any restriction on the time step size, and establish rigorous error estimates in $l^{\infty}(0,T;H^1(\Omega)) \bigcap l^{2}(0,T;H^2(\Omega))$ of orders 1 to 5 in a unified framework.

翻译：本文利用广义标量辅助变量（GSAV）方法，针对Landau-Lifshitz方程构造了新的高阶隐式-显式（IMEX）格式。这些格式为线性格式，具有保长度性，且每时间步仅需求解一个常系数椭圆方程。我们证明了这些格式的数值解在时间步长无限制条件下具有一致有界性，并在统一框架下建立了$l^{\infty}(0,T;H^1(\Omega)) \bigcap l^{2}(0,T;H^2(\Omega))$空间中1至5阶的严格误差估计。