Error analysis of a linear unconditionally energy-stable Leapfrog scheme for the Swift–Hohenberg equation

In this work, we present an energy-stable linear scheme for the Swift–Hohenberg equation based on Leapfrog scheme. We prove rigorously that the scheme satisfies the energy dissipation property. We also prove that our scheme is second-order accurate in time. Moreover, we adopt a spectral-Galerkin approximation for the spatial variables and establish error estimates for the fully discrete scheme. Numerical results are presented to validate our theoretical analysis.