TY - JOUR
T1 - The Structure-Preserving Methods for the Degasperis-Procesi Equation
AU - Zhang , Yuze
AU - Wang , Yushun
AU - Yang , Yanhong
JO - Journal of Computational Mathematics
VL - 4
SP - 475
EP - 487
PY - 2019
DA - 2019/02
SN - 37
DO - http://doi.org/10.4208/jcm.1805-m2017-0184
UR - https://global-sci.org/intro/article_detail/jcm/13003.html
KW - Degasperis-Procesi equation, bi-Hamiltonian structure, Structure-preserving scheme, Fourier pseudospectral method.
AB - <p style="text-align: justify;">This paper gives several structure-preserving schemes for the Degasperis-Procesi equation which has bi-Hamiltonian structures consisted of both complex and non-local Hamiltonian differential operators. For this sake, few structure-preserving schemes have been
proposed so far. In our work, based on one of the bi-Hamiltonian structures, a symplectic
scheme and two new energy-preserving schemes are constructed. The symplecticity comes
straightly from the application of the implicit midpoint method on the semi-discrete system which is proved to remain Hamiltonian, while the energy conservation is derived by
the combination of the averaged vector field method of second and fourth order, respectively. Some numerical results are presented to show that the three schemes do have the
advantages in numerical stability, accuracy in long time computing and ability to preserve
the invariants of the DP equation.</p>