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

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

10.4208/nmtma.OA-2018-0048

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

Preview Full PDF BiBTex 6 418
  • 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.

  • History

Published online: 2019-04

  • AMS Subject Headings

65M10, 78A48

  • Cited by