Arbitrary High-Order Structure-Preserving Schemes for Generalized Rosenau-Type Equations

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.