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 - <p style="text-align: justify;">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.</p>