A High Order Operator Splitting Method for the Degasperis–Procesi Equation

A High Order Operator Splitting Method for the Degasperis–Procesi Equation

Year:    2019

Numerical Mathematics: Theory, Methods and Applications, Vol. 12 (2019), Iss. 3 : pp. 884–905

Abstract

The Degasperis–Procesi equation is split into a system of a hyperbolic equation and an elliptic equation. For the hyperbolic equation, we use the high order finite difference WENO-Z scheme to approximate the nonlinear flux. For the elliptic equation, the wavelet collocation method is employed to discretize the high order derivative. Due to the combination of the WENO-Z reconstruction and the wavelet collocation, the splitting method shows an excellent ability in capturing the formation and propagation of shockpeakon solutions. The numerical simulations for different solutions of the Degasperis–Procesi equation are conducted to illustrate high accuracy and capability of the proposed method.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.OA-2018-0048

Numerical Mathematics: Theory, Methods and Applications, Vol. 12 (2019), Iss. 3 : pp. 884–905

Published online:    2019-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    22

Keywords:    Degasperis–Procesi equation discontinuous solution weighted essentially non-oscillatory method wavelet collocation method.

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