一类非线性偏微分方程的有限差分格式的稳定性问题

The Stability Problem of the Finite Difference Scheme of a Class Partial Nonlinear Differential Equation

对一类非线性偏微分方程进行完全离散,得到非线性有限差分格式.然后引入新的函数空间,并在这个空间上,采用变分近似法讨论了该格式的稳定性问题.文中在给出非线性有限差分格式的稳定性条件时,所用方法具有简单的特点.

In this article, a fully discrete finite nonlinear difference scheme is established for a class of partial nonlinear differential equation. Then the new function space is introduced and the stability problem for the finite difference scheme is discussed by means of variational approximation method in this function space. The approach used is of a simple characteristics in gaining the stability condition of the scheme in the text.