This paper presents a finite difference method combined with the Crank--Nicolson scheme of the Kuramoto--Sivashinsky equation defined on an expanding circle (\cite{KUY}), and the existence, uniqueness, and second-order error estimate of the scheme. The equation can be obtained as a perturbation equation from the circle solution to an interfacial equation and can provide guidelines for understanding the wavenumber selection of solutions to the interfacial equation. Our proposed numerical scheme can help with such a mathematical analysis.

翻译：本文件介绍了一种有限差异法,结合了Kuramoto-Sivashinsky公式的Krank-Nicolson办法,该办法在扩大的圆圈(\\ cite{KUY})上定义,以及该办法的存在、独特性和二级误差估计。该等法可以作为一种从圆形解决方案到中间方程式的扰动方程式获得,并且可以提供指南,用以理解不同方程式解决方案的波数选择。我们提议的数值方法可以帮助进行这样的数学分析。