KMS Of Academy of mathematics and systems sciences, CAS
| The energy-preserving time high-order AVF compact finite difference scheme for nonlinear wave equations in two dimensions | |
| Hou, Baohui1,2; Liang, Dong3 | |
| 2021-12-01 | |
| Source Publication | APPLIED NUMERICAL MATHEMATICS
 |
| ISSN | 0168-9274 |
| Volume | 170Pages:298-320 |
| Abstract | 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. |
| Keyword | AVF method CFD operator Time high-order Energy conservation Convergence Nonlinear wave equations |
| DOI | 10.1016/j.apnum.2021.07.026 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | Natural Sciences and Engineering Research Council of Canada ; China Postdoctoral Science Foundation[2021M693339] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000695210800018 |
| Publisher | ELSEVIER |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/59234 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Liang, Dong |
| Affiliation | 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 |
| Recommended Citation 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. |
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