Arbitrary high-order structure-preserving schemes for generalized Rosenau-type equations. (English) Zbl 1538.65418
Summary: 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.
MSC:
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65P10 | Numerical methods for Hamiltonian systems including symplectic integrators |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
Keywords:
momentum-preserving; energy-preserving; high-order; symplectic Runge-Kutta method; Rosenau equationReferences:
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