East Asian J. Appl. Math., 13 (2023), pp. 935-959.
Published online: 2023-10
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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} }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.