Annals of Mathematical Sciences and Applications
Volume 2 (2017)
Guest Editors: Tai-Chia Lin (National Taiwan University), Wen-Wei Lin (National Chiao Tung University), Tony Wen-Hann Sheu (National Taiwan University), Weichung Wang (National Taiwan University), Chih-wen Weng (National Chiao Tung University), and Salil Vadhan (Harvard University).
Weighted essentially non-oscillatory schemes for Degasperis–Procesi equation with discontinuous solutions
Pages: 319 – 340
In this paper, we develop the high order weighted essentially nonoscillatory (WENO) schemes for solving the Degasperis–Procesi (DP) equation, including finite volume (FV) and finite difference (FD) methods. The DP equation contains nonlinear high order derivatives, and possibly discontinuous or sharp transition solutions. The finite volume method is designed based on the total variation bounded property of the DP equation. And the finite difference method is constructed based on the $L^2$ stability of the DP equation. Due to the adoption of the WENO reconstruction, both schemes are arbitrary high order accuracy and shock capturing. The numerical simulation results for different types of solutions of the nonlinear Degasperis–Procesi equation are provided to illustrate the accuracy and capability of the methods.
Degasperis–Procesi equation, discontinuous solution, weighted essentially non-oscillatory schemes, finite difference method, finite volume method
2010 Mathematics Subject Classification
Primary 65M06, 65M08. Secondary 35Q53.
Y. Xia’s research supported by NSFC grant No. 11371342, No. 11471306.
Y. Xu’s research supported by NSFC grant No. 11371342, No. 11526212.
Received 27 June 2016
Published 10 August 2017