The error estimations of a two-level linearized compact ADI method for solving the nonlinear coupled wave equations

被引:4
|
作者
Deng, Dingwen [1 ]
Wu, Qiang [2 ]
机构
[1] Nanchang Hangkong Univ, Coll Math & Informat Sci, Nanchang 330063, Jiangxi, Peoples R China
[2] Jiangxi Normal Univ, Coll Sci & Technol, Jiujiang 332020, Peoples R China
基金
中国国家自然科学基金;
关键词
Nonlinear coupled sine-Gordon equations; Nonlinear coupled Klein-Gordon equations; Compact ADI method; Error estimations; HIGH-ORDER ALGORITHM; DIFFUSION EQUATIONS; GORDON EQUATIONS; SCHEME; SYSTEM; ENERGY; SPACE;
D O I
10.1007/s11075-021-01168-9
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this article, a two-level linearized compact alternating direction implicit (ADI) scheme is proposed for solving two-dimensional (2D) nonlinear coupled wave equations (NCWEqs). In comparison with the existent compact ADI methods for NCWEqs, there are two obvious characters. (1) Numerical solutions at time level one, which have effect on the global stability and convergence of the numerical solutions, are not needed to be solved firstly by using another numerical scheme. (2) The computational cost is comparatively low and acceptable because the new compact ADI method is a linear scheme, thus avoiding Newton's iterations. By using the energy analysis method, it is shown that numerical solutions converge to exact solutions with an order of O(Delta t(2) + h(x)(4) + h(y)(4)) in H-1- and L-infinity-norms, and are uniquely solvable. Numerical examples are given to illustrate the exactness of the theoretical findings and the high-performance of our methods.
引用
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页码:1663 / 1693
页数:31
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