In this paper, we apply the high-order compact scheme coupled with alternating direction implicit (HOC–ADI) method to solve the two-dimensional Ginzburg–Landau (2D GL) equation. Five HOC–ADI schemes with second order accuracy in time and fourth order in space are proposed for 2D GL equation. Scheme I and Scheme II are both nonlinear, which need nonlinear iteration.To overcome this shortcoming, Scheme III and Scheme IV are proposed in order to avoid nonlinear iteration. With the three-level ADI scheme and the method of extrapolation, we obtain a linearized scheme V. Some numerical experiments are shown to testify and compare the superiority of the new numerical schemes.

在本文中，我们应用高阶紧致方案与交替方向隐式 (HOC-ADI) 方法相结合来求解二维 Ginzburg-Landau (2D GL) 方程。为二维 GL 方程提出了五种具有时间二阶精度和空间四阶精度的 HOC-ADI 方案。方案一和方案二都是非线性的，需要非线性迭代。为了克服这个缺点，提出方案三和方案四以避免非线性迭代。利用三级ADI方案和外推法，我们得到了一个线性化方案V。一些数值实验证明和比较了新数值方案的优越性。