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

页码：273 / 291

页数：19

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