Stability and error analysis of linear IMEX schemes for sixth-order Cahn–Hilliard-type equations

Abstract

In this paper, we develop efficient implicit-explicit (IMEX) schemes for solving sixth-order Cahn–Hilliard-type equations based on the generalized scalar auxiliary variable (GSAV) approach. These novel schemes provide several remarkable advantages: (i) they are linear and only require solving one elliptic equation with constant coefficients at each time step; (ii) they are unconditionally energy stable and yield a uniform bound for the numerical solution. We also establish rigorous error estimates of up to fifth-order for these schemes, and present various numerical experiments to validate the stability and accuracy of the proposed schemes.