一类多维非线性反应扩散方程有限差分格式的稳定性分析

Analysis of the Stability of Finite Difference Scheme for a Multidimensional Nonlinear Reaction-Diffusion Equation

对一类多维非线性反应扩散方程进行完全离散,得到完全离散的非线性有限差分格式.然后,引入步长函数空间,并在这个空间上,利用变分近似法讨论该格式的稳定性问题.在给出非线性有限差分格式的稳定性条件时,所使用方法非常简单、有效.

In the article,the fully discrete finite difference scheme for a multidimensional nonlinear reaction-diffusion equation is established.Then the step function space is introduced and the stability problem for the finite difference scheme is discussed by means of variational approximation.The approach used is extraordinary simplicity and availability in gaining the stability condition of the scheme.