The energy-preserving time high-order AVF compact finite difference scheme for nonlinear wave equations in two dimensions

doi:10.1016/j.apnum.2021.07.026

CSpace

	The energy-preserving time high-order AVF compact finite difference scheme for nonlinear wave equations in two dimensions
	Hou, Baohui 1,2; Liang, Dong 3
	2021-12-01
发表期刊	APPLIED NUMERICAL MATHEMATICS
ISSN	0168-9274
卷号	170 页码:298-320
摘要	In this paper, energy-preserving time high-order average vector field (AVF) compact finite difference scheme is proposed and analyzed for solving two-dimensional nonlinear wave equations including the nonlinear sine-Gordon equation and the nonlinear Klein-Gordon equation. We first present the corresponding Hamiltonian system to the two-dimensional nonlinear wave equations, and further apply the compact finite difference (CFD) operator and AVF method to develop an energy conservative high-order scheme in two dimensions. The L-p-norm boundedness of two-dimensional numerical solution is obtained from the energy conservation property, which plays an important role in the analysis of the scheme for the two-dimensional nonlinear wave equations in which the nonlinear term satisfies local Lipschitz continuity condition. We prove that the proposed scheme is energy conservative and uniquely solvable. Furthermore, optimal error estimate for the developed scheme is derived for the nonlinear sine-Gordon equation and the nonlinear Klein-Gordon equation in two dimensions. Numerical experiments are carried out to confirm the theoretical findings and to show the performance of the proposed method for simulating the propagation of nonlinear waves in layered media. (C) 2021 IMACS. Published by Elsevier B.V. All rights reserved.
关键词	AVF method CFD operator Time high-order Energy conservation Convergence Nonlinear wave equations
DOI	10.1016/j.apnum.2021.07.026
收录类别	SCI
语种	英语
资助项目	Natural Sciences and Engineering Research Council of Canada ; China Postdoctoral Science Foundation[2021M693339]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000695210800018
出版者	ELSEVIER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/59234
专题	中国科学院数学与系统科学研究院
通讯作者	Liang, Dong
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, Beijing 100190, Peoples R China 2.Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China 3.York Univ, Dept Math & Stat, Toronto, ON M3J 1P3, Canada
推荐引用方式 GB/T 7714	Hou, Baohui,Liang, Dong. The energy-preserving time high-order AVF compact finite difference scheme for nonlinear wave equations in two dimensions[J]. APPLIED NUMERICAL MATHEMATICS,2021,170:298-320.
APA	Hou, Baohui,&Liang, Dong.(2021).The energy-preserving time high-order AVF compact finite difference scheme for nonlinear wave equations in two dimensions.APPLIED NUMERICAL MATHEMATICS,170,298-320.
MLA	Hou, Baohui,et al."The energy-preserving time high-order AVF compact finite difference scheme for nonlinear wave equations in two dimensions".APPLIED NUMERICAL MATHEMATICS 170(2021):298-320.