A second-order linear and unconditional energy-stable scheme for Swift-Hohenberg equations

In the paper, an unconditional energy-stable scheme is developed with the help of the scalar auxiliary variable (SAV) approach and the leapfrog time-discretization. The fully discrete scheme gives a linear and decoupled system, whereas previous SAV-type methods usually gave a coupled linear system. Therefore, the proposed scheme is decoupled and thus easier to be implemented. Moreover, it is proved that the proposed scheme has second-order time accuracy in the temporal direction. Several numerical examples are provided to support the proposed theoretical results.