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. • A linear scheme for the SH equation based on Leapfrog scheme is proposed. • The energy dissipation property of the scheme is proved rigorously. • Error estimates for the fully discrete scheme is established. • Numerical results are presented to validate our theoretical analysis. [ABSTRACT FROM AUTHOR]