SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Contributed Talk

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Two new schemes for the Degasperis-Procesi equation

W. Cai and Y. Sun

Abstract
Two new numerical schemes are proposed to solve the Degasperis-Procesi equation. One is a symplectic integrator which preserves invariants very well. The other is constructed by the splitting method which can handle with the shockpeakon cases while the first one cannot. Fifth-order WENO scheme and multisymplectic pseudospectral method are involved in the construction of the splitting method. It also shows nice properties in invariant preservation. Various numerical tests are presented to show the advantages of these two schemes with respect to different kind of solutions.

Bibliography
[1] A. Degasperis, D.D. Holm and A.H.W. Hone, A new integrable equation with peakon solutions, Theor. Math. Phys., 133 (2002), pp. 1463-1474.
[2] H. Lundmark, Formation and dynamics of shock waves in the Degasperis-Procesi equation, J. Nonlinear. Sci., 17 (2007), pp. 169-198.
[3] B.F. Feng and Y. Liu, An operator splitting method for the Degasperis-Procesi equation, J. Comput. Phys., 228 (2009), pp. 7805-7820.
[4] T.J. Bridges and S. Reich, Numerical methods for Hamiltonian PDEs, J. Phys. A, 39 (2006), pp. 5287-5320.

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