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.