二维二阶双曲型方程隐式差分格式的稳定性分析  

Stability analysis of implicit difference schemes for second order hyperbolic equations in two dimensions

作　　者：吴泽康 韩文静 耿勇 王晓丽[1] WU Zekang;HAN Wenjing;GENG Yong;WANG Xiaoli(School of Mathematics and Statistics,Qilu University of Technology(Shandong Academy of Sciences),Jinan 250353,China)

机构地区：[1]齐鲁工业大学(山东省科学院)数学与统计学院,山东济南250353

出　　处：《齐鲁工业大学学报》2023年第1期75-80,共6页Journal of Qilu University of Technology

基　　金：国家自然科学基金(11801292);山东省自然科学基金(ZR2019PA020、ZR2020MA049)。

摘　　要：研究了二维二阶双曲型方程交替方向隐式差分格式的稳定性问题。利用分离变量法给出了两种计算特征方程的方法,并对差分格式的稳定性做了详细讨论。结果表明在不同的权重下,差分格式的稳定性与网格比取值有关。The stability of alternating directions implicit difference scheme for two-dimensional second-order hyperbolic equations is studied.With the help of the method of separating variables,two methods for calculating the characteristic equation are given,and the stability of difference schemes is discussed in detail.The results show that the stability of the difference scheme is related to the grid ratio under different weights.

关 键 词：有限差分法 双曲型方程 分离变量法 稳定性分析 

分 类 号：O241.84[理学—计算数学]