Modified Structure-Preserving Schemes for the Degasperis—Procesi Equation*
2016
We investigate the structure-preserving numerical algorithm of the Degasperis—Procesi equation which can be transformed into a bi-Hamiltonian form using the discrete variational derivative method. Based on two different space discretization methods, the Fourier pseudospectral method and the wavelet collocation method, we develop two modified structure-preserving schemes under the periodic boundary condition. These proposed schemes are proved to preserve the Hamiltonian invariants theoretically and numerically. Meanwhile, the numerical results confirm that they can simulate the propagation of solitons effectively for a long time.
Keywords:
- Pseudo-spectral method
- Mathematical analysis
- Hamiltonian (quantum mechanics)
- Discretization
- Degasperis–Procesi equation
- Functional derivative
- Optics
- Fourier transform
- Physics
- Wavelet
- Collocation method
- fourier pseudospectral method
- Periodic boundary conditions
- Atomic physics
- Applied mathematics
- Invariant (mathematics)
- Soliton
- Correction
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