Modified Structure-Preserving Schemes for the Degasperis–Procesi Equation
Ming-Zhan Song, Xu Qian, Song-He Song**
College of Science and State Key Laboratory of High Performance Computing, National University of Defense Technology, Changsha 410073
Abstract ：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.
收稿日期: 2016-05-26
出版日期: 2016-11-28
:
02.30.Jr
(Partial differential equations)
02.30.Sa
(Functional analysis)
02.60.Cb
(Numerical simulation; solution of equations)
02.60.Jh
(Numerical differentiation and integration)
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2016, Vol. 33 
