Rosenau-Burgers方程的修正局部Crank-Nicolson格式  

The Modified Local Crank-Nicolson Schemes for Rosenau-Burgers Equation

作　　者：穆耶赛尔·艾合麦提 阿布都热西提·阿布都外力[1] 阿不都艾尼·阿不都西库尔 Muyassar Ahmat;Abdurishit Abduwali;Abdugeni Abduxkur(-College of Mathematics and System Science,Xinjiang University,Urumqi 830046;-College of Mathematics and Statistics,Yili Normal University,Yining 835000)

机构地区：[1]新疆大学数学与系统科学学院,乌鲁木齐830046 [2]伊犁师范大学数学与统计学院,伊宁835000

出　　处：《工程数学学报》2020年第2期231-244,共14页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10971024).

摘　　要：本文给出了Rosenau-Burgers方程的两种修正局部Crank-Nicolson格式.首先,求解原有的偏微分方程对空间方向进行有限差分离散而得到的常微分方程.其次,利用矩阵分裂技术对这个方程的指数系数矩阵分别按行和元素进行逼近.最后,利用修正局部Crank-Nicolson方法得到了两种格式.讨论了格式的稳定性、收敛性和先验误差估计.数值实验结果表明了理论证明的正确性及格式的有效性.该格式具有结构简单、精度高的优点.Two class of modified local Crank-Nicolson schemes for Rosenau-Burgers equation are proposed.Firstly,we obtain the exact solution of the ODE which reached from the original PDE by using central finite difference discretization in space direction.Next,the exponential coefficient matrix of this equation is approximated by using matrix splitting technique by line and element.Finally,two types of methods are achieved by using modified local Crank-Nicolson scheme.The stability,convergence and priori error estimation of two schemes are discussed.The accuracy of theoretical proof and efficiency of both schemes are demonstrated by numerical results.The proposed methods possess the advantages of simple structure and high accuracy.

关 键 词：Rosenau-Burgers方程 Crank-Nicolson方法 修正局部Crank-Nicolson格式 

分 类 号：O241.82[理学—计算数学]