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Volume 12, Issue 3
A High Order Operator Splitting Method for the Degasperis–Procesi Equation

Yunrui Guo, Hong Zhang, Wenjing Yang, Ji Wang & Songhe Song

DOI: 10.4208/nmtma.OA-2018-0048

Numer. Math. Theor. Meth. Appl., 12 (2019), pp. 884-905.

Published online: 2019-04

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  • 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.

  • Keywords

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

  • AMS Subject Headings

65M10, 78A48

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-12-884, author = {Yunrui Guo, Hong Zhang, Wenjing Yang, Ji Wang and Songhe Song}, title = {A High Order Operator Splitting Method for the Degasperis–Procesi Equation}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2019}, volume = {12}, number = {3}, pages = {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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2018-0048}, url = {http://global-sci.org/intro/article_detail/nmtma/13135.html} }
TY - JOUR T1 - A High Order Operator Splitting Method for the Degasperis–Procesi Equation AU - Yunrui Guo, Hong Zhang, Wenjing Yang, Ji Wang & Songhe Song JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 884 EP - 905 PY - 2019 DA - 2019/04 SN - 12 DO - http://doi.org/10.4208/nmtma.OA-2018-0048 UR - https://global-sci.org/intro/article_detail/nmtma/13135.html KW - Degasperis–Procesi equation, discontinuous solution, weighted essentially non-oscillatory method, wavelet collocation method. AB -

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.

Yunrui Guo, Hong Zhang, Wenjing Yang, Ji Wang and Songhe Song. (2019). A High Order Operator Splitting Method for the Degasperis–Procesi Equation. Numerical Mathematics: Theory, Methods and Applications. 12 (3). 884-905. doi:10.4208/nmtma.OA-2018-0048
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