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Weighted essentially non-oscillatory schemes for Degasperis-Procesi equation with discontinuous solutions

Yinhua Xia University of Science and Technology of China Yan Xu University of Science and Technology of China

Numerical Analysis and Scientific Computing mathscidoc:1612.25006

Annals of Mathematical Sciences and Applications, 2016.11
In this paper, we develop the high order weighted essentially non-oscillatory (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 de- signed based on the total variation bounded property of the DP equation. And the finite difference method is constructed based on the L2 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.
[ Download ] [ 2016-12-31 21:50:43 uploaded by yhxia ] [ 1553 downloads ] [ 0 comments ] 
@inproceedings{yinhua2016weighted,
  title={Weighted essentially non-oscillatory schemes for Degasperis-Procesi equation with discontinuous solutions},
  author={Yinhua Xia, and Yan Xu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161231215043106913702},
  booktitle={Annals of Mathematical Sciences and Applications},
  year={2016},
}
Yinhua Xia, and Yan Xu. Weighted essentially non-oscillatory schemes for Degasperis-Procesi equation with discontinuous solutions. 2016. In Annals of Mathematical Sciences and Applications. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161231215043106913702.
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