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

作　　者：徐琛梅[1] 杨巍纳[1] 

机构地区：[1]河南大学数学与信息科学学院,河南开封475001

出　　处：《河南大学学报（自然科学版）》2008年第3期228-230,242,共4页Journal of Henan University:Natural Science

摘　　要：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.

关 键 词：有限差分格式 稳定性问题 变分近似法 反应扩散方程 

分 类 号：O241.84[理学—计算数学]