带非线性强迫项的Burgers方程二阶收敛的差分格式  

A Second-Order Difference Scheme for Burgers' Equation with Nonlinear Force

作　　者：艾尧[1] 吴宏伟[1] 

机构地区：[1]东南大学数学系,江苏南京210096

出　　处：《应用数学》2010年第1期116-124,共9页Mathematica Applicata

基　　金：国家自然科学基金资助项目(10871044)

摘　　要：本文研究带非线性强迫项的Burguers方程初边值问题的有限差分方法.构造了一个两层线性化隐式差分格式.证明了差分格式解的存在唯一性、收敛性和稳定性.并给出了差分解在L∞模意义下的收敛阶数为O(h2+τ2).数值例子验证了理论分析结果.A finite difference scheme for Burgers equation with nonlinear force is proposed and analyzed.The scheme constructed in this paper is a two-level and linearized scheme.The order of accuracy is second-order in both time and space.It is shown that the difference scheme is uniquely solvable and convergent and stable in L∞ norm.Some numerical experiments are conducted to illustrate the theoretical results of the presented method.

关 键 词：BURGERS方程 差分格式 收敛性 稳定性 

分 类 号：O241.82[理学—计算数学]