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 - <p style="text-align: justify;">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.</p>