Chaolong Jiang, Xu Qian, Songhe Song and Chenxuan Zheng
{"title":"Arbitrary High-Order Structure-Preserving Schemes for Generalized Rosenau-Type Equations","authors":"Chaolong Jiang, Xu Qian, Songhe Song and Chenxuan Zheng","doi":"10.4208/eajam.2022-308.300123","DOIUrl":null,"url":null,"abstract":". Arbitrary high-order numerical schemes conserving the momentum and energy of the generalized Rosenau-type equation are studied. Derivation of momentum-preserving schemes is made within the symplectic Runge-Kutta method coupled with the standard Fourier pseudo-spectral method in space. Combining quadratic auxiliary variable approach, symplectic Runge-Kutta method, and standard Fourier pseudo-spectral method, we introduce a class of high-order mass-and energy-preserving schemes for the Rosenau equation. Various numerical tests illustrate the performance of the proposed schemes.","PeriodicalId":48932,"journal":{"name":"East Asian Journal on Applied Mathematics","volume":"13 1","pages":"0"},"PeriodicalIF":1.2000,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"East Asian Journal on Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4208/eajam.2022-308.300123","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
. Arbitrary high-order numerical schemes conserving the momentum and energy of the generalized Rosenau-type equation are studied. Derivation of momentum-preserving schemes is made within the symplectic Runge-Kutta method coupled with the standard Fourier pseudo-spectral method in space. Combining quadratic auxiliary variable approach, symplectic Runge-Kutta method, and standard Fourier pseudo-spectral method, we introduce a class of high-order mass-and energy-preserving schemes for the Rosenau equation. Various numerical tests illustrate the performance of the proposed schemes.
期刊介绍:
The East Asian Journal on Applied Mathematics (EAJAM) aims at promoting study and research in Applied Mathematics in East Asia. It is the editorial policy of EAJAM to accept refereed papers in all active areas of Applied Mathematics and related Mathematical Sciences. Novel applications of Mathematics in real situations are especially welcome. Substantial survey papers on topics of exceptional interest will also be published occasionally.