提出了一种用于时空方程时间离散化的指数谱过程 (ESP) 方法。提出的 ESP方法在每个时间步骤中使用显式迭代，这允许我们在每个迭代中使用简单的常数初始化。这种方法能够以合理的大时间步长获得较高的精度 (达到机器精度)。为了验证 ESP 方法的优点，我们考虑了在大时间模拟中存在稳定性困难的两个应用。其中一个是 Allen-Cahn 方程，它的对称性破缺问题与现有的大多数时间离散都面临的问题，另一个是复的 Ginzburg-Landau 方程，它也存在较大的时间不稳定性。

We propose an exponential spectral process (ESP) method for time discretization of spacial-temporal equations. The proposed ESP method uses explicit iterations at each time step, which allows us to use simple initializations at each iteration. This method has the capacity to obtain high accuracy (up to machine precision) with reasonably large time step sizes. To demonstrate the advantages of the ESP method, we consider two applications which have stability difficulties in large time simulations. One of them is the Allen-Cahn equation with the symmetry breaking problem faced by most of the existing time discretizations, and the second one is about the complex Ginzburg-Landau equation which also suffers from large time instability