一个类似Burgers方程的数值解  

Numerical Solution of a Burgers-like Equation

作　　者：盛秀兰[1,2] 艾尧[1] 吴宏伟[1] 

机构地区：[1]东南大学数学系,江苏南京210096 [2]江苏广播电视大学公共课教学部,江苏南京210036

出　　处：《郑州大学学报（理学版）》2010年第3期23-26,共4页Journal of Zhengzhou University:Natural Science Edition

基　　金：国家自然科学基金资助项目;编号10871044

摘　　要：研究了一个类似Burgers方程的初边值问题的有限差分方法.基于Crank-Nicolson方法,建立了一个两层线性化隐式差分格式,讨论了差分格式的可解性.利用离散能量估计方法证明了差分解在最大模意义下关于时间和空间的二阶收敛性,并用数值算例验证了理论分析结果.A second-order finite difference scheme for a Burgers-like equation is proposed and analyzed.The scheme constructed is a double-deck linearized scheme that can be solved easily by Thomas＇ algorithm.The solvability of difference scheme is obtained.It is shown that the difference scheme is convergent in maximum norm.The convergence order is second-order in both space and time.Some numerical experiments are conducted to illustrate the theoretical results of the presented method.

关 键 词：类似Burgers方程 隐式差分格式 收敛性 离散能量估计 

分 类 号：O241.82[理学—计算数学]