Kdv-Burgers方程的两层线性化隐式差分格式  

A two-level and linearized implicit difference scheme for the Kdv-Burgers' equation

作　　者：盛秀兰[1,2] 吴宏伟[2] 

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

出　　处：《扬州大学学报（自然科学版）》2013年第1期17-21,共5页Journal of Yangzhou University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11071039);江苏广播电视大学"十二五"规划课题(12SEW-C-109)

摘　　要：应用非线性对流项和反应项的两层线性化技巧,对非线性Kdv-Burgers方程周期边界问题构建了一类具有二阶截断误差的两层线性化隐式差分格式.用数学归纳原理和离散能量法建立了差分格式的唯一可解性、在最大模意义下的收敛性和稳定性.数值计算表明,该格式在时间和空间上都是二阶收敛的.Based on two-level linearized technique for nonlinear convection and reaction term, a twolevel linearized implicit difference scheme with second-order truncation error is presented for the periodic boundary problem of nonlinear Kdv-Burgers equations. The unique solvability, convergence and stability in the maximum norm of difference scheme are obtained by mathematical induction and discrete energy methods. It is shown by numerical experiments that the scheme is second- order convergent in both space and time.

关 键 词：Kdv—Burgers方程 隐式差分格式 收敛性 稳定性 

分 类 号：O241.82[理学—计算数学]