中文摘要：

本文首先对一类八阶变系数微分方程建立了有限差分格式，并将该格式表示成矩阵的形式。然后，利用矩阵特征值和范数的理论，证明该格式解的收敛性和唯一性。借助数值算例说明该格式既有效、又便于模拟。另外，文中所用方法还能用于应用中的某些非线性微分方程问题的研究。

英文摘要：

In this article, a finite difference scheme for a class of eighth-order dif ferential equations with variable coefficients is established. The scheme is rewritten in a matrix form. The convergence and uniqueness of the solution to the scheme are proved by means of the matrix eigenvalue and norm theory. A numerical example shows that the method is very effective and simple to implement. In addition, the method can be applied to the study of some nonlinear differential equations arising in app-lications.