解对流占优反应扩散问题一致稳定的差分格式  

A uniformly stable difference scheme for solving the convection-dominated reaction-diffusion problems

作　　者：张铁[1] 王宝艳[1] 

机构地区：[1]东北大学数学系,辽宁沈阳110004

出　　处：《高校应用数学学报（A辑）》2010年第2期195-201,共7页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(10771031)

摘　　要：通过将一般的反应扩散方程转化为主部为守恒型方程形式,构造出一种稳定和高精度的新型差分格式.这种差分格式最大的优点是具有与方程Peclet数和网格步长无关的一致稳定性,特别适合求解强对流占优问题或边界层问题.同时还给出了差分格式按L_∞模的一致稳定性和O(h^2)阶收敛速度的理论分析.数值实验验证了理论分析结果.By transforming the reaction-diffusion equations into a conservation form, a stable and high accuracy difference scheme was constructed. The main advantage of this scheme is that it possesses the uniform stability independent of the Peclet number of equation and the mesh size, which is very suitable for solving the convection-dominated problems or boundary layer problems. A complete theoretical analysis was given to demonstrate the uniform stability and O（h^2）-order convergence rate under L∞ norm. Numerical experiments verify the theoretical analysis results.

关 键 词：强对流占优问题 差分方法 一致稳定性 误差分析 

分 类 号：O241.82[理学—计算数学]