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.

中文翻译：

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Swift-Hohenberg 方程的二阶线性无条件能量稳定格式

在本文中，借助标量辅助变量（SAV）方法和蛙跳时间离散化，提出了一种无条件能量稳定方案。完全离散方案给出了线性解耦系统，而以前的 SAV 类型方法通常给出了耦合线性系统。因此，所提出的方案是解耦的，因此更容易实现。此外，证明了该方案在时间方向上具有二阶时间精度。提供了几个数值例子来支持所提出的理论结果。