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

	The energy-preserving time high-order AVF compact finite difference scheme for nonlinear wave equations in two dimensions
	Hou, Baohui 1,3; Liang, Dong 2
刊名	APPLIED NUMERICAL MATHEMATICS
	2021-12-01
卷号	170 页码:298-320
关键词	AVF method CFD operator Time high-order Energy conservation Convergence Nonlinear wave equations
ISSN号	0168-9274
DOI	10.1016/j.apnum.2021.07.026
英文摘要	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.
资助项目	Natural Sciences and Engineering Research Council of Canada ; China Postdoctoral Science Foundation[2021M693339]
WOS研究方向	Mathematics
语种	英语
出版者	ELSEVIER
WOS记录号	WOS:000695210800018
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/59233]
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.York Univ, Dept Math & Stat, Toronto, ON M3J 1P3, Canada 3.Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China
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.