Analysis of a fourth-order compact ADI method for a linear hyperbolic equation with three spatial variables

被引:10
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
关键词
Telegraph wave equation; Compact finite difference scheme; ADI method; Convergence; FINITE-DIFFERENCE SCHEME; HEAT-TRANSPORT EQUATION; TELEGRAPH EQUATION; ORDER;
D O I
10.1007/s11075-012-9604-8
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This paper is concerned with a three-level alternating direction implicit (ADI) method for the numerical solution of a 3D hyperbolic equation. Stability criterion of this ADI method is given by using von Neumann method. Meanwhile, it is shown by a discrete energy method that it can achieve fourth-order accuracy in both time and space with respect to H-1- and L-2-norms only if stable condition is satisfied. It only needs solution of a tri-diagonal system at each time step, which can be solved by multiple applications of one-dimensional tri-diagonal algorithm. Numerical experiments confirming the high accuracy and efficiency of the new algorithm are provided.
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页码:1 / 26
页数:26
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