  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.
