Application of a fourth-order compact ADI method to solve a two-dimensional linear hyperbolic equation

被引：21
|
作者：
Deng, Dingwen [1 ,2 ]
Zhang, Chengjian [1 ]
机构：
[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China
[2] Nanchang Hangkong Univ, Coll Math & Informat Sci, Nanchang 330063, Peoples R China
来源：
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2013年 / 90卷 / 02期
关键词：
hyperbolic equation; compact finite difference scheme; ADI method; stability; convergence; solvability; 65M06; 65M12; 65M15; FINITE-DIFFERENCE SCHEME; HEAT-TRANSPORT EQUATION; TELEGRAPH EQUATION; WAVE-EQUATION; HIGHER-ORDER; THIN-FILM;
D O I：
10.1080/00207160.2012.713475
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, a compact alternating direction implicit method is developed for solving a linear hyperbolic equation with constant coefficients. Its stability criterion is determined by using von Neumann method. It is shown through a discrete energy method that this method can attain fourth-order accuracy in both time and space with respect to H 1- and L 2-norms provided the stability condition is fulfilled. Its solvability is also analysed in detail. Numerical results confirm the convergence orders and efficiency of our algorithm.
引用
收藏
页码：273 / 291
页数：19
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