Swift-Hohenberg方程因其本身的复杂性和其解演化形成有趣模式的过程，广受学界的关注。本项目研究SH方程的高效数值算法。首先，通过考虑有限元，有限差分等空间离散方法和算子分裂、半隐式格式和高阶的时间格式，选取具有一定时空精度的格式离散SH方程。在此基础上选择格式，使离散方程保持非线性稳定性和其他一些物理性质。对长时间模拟行为，提出新的时间步长预测的方法，以及使用已有的PI控制法，并注意避免已有方法中含有人工参数选取的缺陷。最后，通过编写程序实现有限元和有限差分的数值计算，加入步长预测方法和PI控制法的模块预测计算步长，利用非线性求解器求解方程。通过与已有的方法进行比较，体现本项目的方法是高效的数值方法。

The Swift-Hohenberg (SH) equation has attracted much attention and research from scholars due to the complex form of its equation as well as the interesting pattern formation process it evolves. In this project, we focus on efficient numerical method for SH equation. First, with finite element method and finite difference method to discretize the space variable, and operator splitting method, semi-implicit method and high order scheme to discretize temporal variable, some discrete schemes with adequate accuracy in both space and time are proposed. Based on these schemes, we choose ones that keep a discreet version of nonlinear stability property, and some other physical properties as well. For long time simulation, a new time-step prediction method is proposed, and also the PI controller method is used. In the new method, we prevent the artificial parameter problem in the existing method. At last, the finite difference scheme and finite element scheme is implemented. The time-step perdition module and PI controller module are introduced, and some existing nonlinear solvers are also used. Compared with the existing methods, the project here is showed to be efficient numerical methods for SH equation.