对流占优扩散方程的几个特征差分格式  

Characteristics Difference Schemes for Diffusion Equation with Significant Convection

作　　者：柏琰[1] 

机构地区：[1]南京晓庄学院教育科学学院,江苏南京210038

出　　处：《南京晓庄学院学报》2007年第6期7-10,共4页Journal of Nanjing Xiaozhuang University

摘　　要：文章研究了一类线性对流占优扩散方程的初边值问题.采用了A.A.Samarskii构造差分格式的思想,对方程的扩散项进行修正,构造了线性对流占优扩散方程的显、隐式特征差分格式和C-N格式,三个格式的收敛阶均为O(+h2),利用Fourier方法分析论证了其稳定性和收敛性.An initial-boundary value problem of convection-dominated diffusion equation is considered in this paper. The Samarskii＇s perturbation method is used to deal with the term of diffusion and the explicit, implicit and C- N schemes are proposed. The stability and convergence of the three schemes are discussed in this paper. Convergence and stability of difference scheme are proved in the order of O（τ ＋ h^2）.

关 键 词：对流占优扩散方程 特征差分格式 收敛性 稳定性 

分 类 号：O241.8[理学—计算数学]