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Volume 13, Issue 4
Arbitrary High-Order Structure-Preserving Schemes for Generalized Rosenau-Type Equations

Chaolong Jiang, Xu Qian, Songhe Song & Chenxuan Zheng

DOI: 10.4208/eajam.2022-308.300123

East Asian J. Appl. Math., 13 (2023), pp. 935-959.

Published online: 2023-10

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  • 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.

  • Keywords

Momentum-preserving, energy-preserving, high-order, symplectic Runge-Kutta method, Rosenau equation.

  • AMS Subject Headings

65M06, 65M70

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-13-935, author = {Jiang , ChaolongQian , XuSong , Songhe and Zheng , Chenxuan}, title = {Arbitrary High-Order Structure-Preserving Schemes for Generalized Rosenau-Type Equations}, journal = {East Asian Journal on Applied Mathematics}, year = {2023}, volume = {13}, number = {4}, pages = {935--959}, 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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.2022-308.300123}, url = {http://global-sci.org/intro/article_detail/eajam/22069.html} }
TY - JOUR T1 - Arbitrary High-Order Structure-Preserving Schemes for Generalized Rosenau-Type Equations AU - Jiang , Chaolong AU - Qian , Xu AU - Song , Songhe AU - Zheng , Chenxuan JO - East Asian Journal on Applied Mathematics VL - 4 SP - 935 EP - 959 PY - 2023 DA - 2023/10 SN - 13 DO - http://doi.org/10.4208/eajam.2022-308.300123 UR - https://global-sci.org/intro/article_detail/eajam/22069.html KW - Momentum-preserving, energy-preserving, high-order, symplectic Runge-Kutta method, Rosenau equation. AB -

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.

Jiang , ChaolongQian , XuSong , Songhe and Zheng , Chenxuan. (2023). Arbitrary High-Order Structure-Preserving Schemes for Generalized Rosenau-Type Equations. East Asian Journal on Applied Mathematics. 13 (4). 935-959. doi:10.4208/eajam.2022-308.300123
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