一类多维非线性反应扩散方程有限差分格式的稳定性问题

摘要

In this paper,stability of the difference scheme for a multidimensional nonlinear reaction-diffusion equation is studied.Using incremental unknowns method,the finite difference scheme with incremental unknowns is established.Then the stability condition of the scheme is obtained by means of nonlinear Galerkin method.Through stability analysis for the scheme,it is shown that stability of the finite difference scheme with the incremental unknowns is improved when compared with that of the corresponding classical difference scheme.%本文研究了一类多维线性反应扩散方程差分格式的稳定性.利用量未知元方法,建立了具有增量未知元的有限差分格式；然后利用非线性Galerkin方法,得到该差分格式的稳定性条件.通过对该格式的稳定性分析,说明和经典的差分格式的稳定性相比较,带有增量未知元的有限差分格式的稳定性得到了提高.