抛物型微分方程的Crank-Nicolson块中心差分方法  

Crank-Nicolson Block-centered Difference Scheme For Parabolic Problems

作　　者：任宗修[1] 张秀春[1] 银召利[1] 

机构地区：[1]河南师范大学数学与信息科学学院,河南新乡453007

出　　处：《河南师范大学学报（自然科学版）》2011年第1期15-19,共5页Journal of Henan Normal University(Natural Science Edition)

基　　金：国家自然科学基金(10671057)

摘　　要：针对有界区域上的抛物型微分方程讨论了Crank-Nicolson块中心差分法,在非等距剖分的网格上得了近似解和解的一阶导数的L2模误差估计,重要的是提高了时间上的精度.数值试验结果与理论分析一致,说明格式具有高效的收敛性.This paper considers the Crank-Nicolson block-centered difference method for the solution of the linear parabolic differential problems in the bounded domain.The research gets the discrete L2-norm errors in both the approximate solution and its first derivatives for all nonuniform grids,with sufficiently smooth data.It is important to get higher precision in time than the block-centered finite difference method.It is the same time to have the same result in the numerical experiment and the theorem.

关 键 词：抛物型微分方程 Crank-Nicolson块中心差分方法 误差估计 

分 类 号：O241.82[理学—计算数学]