High Order Finite Difference WENO Methods with Unequal-Sized Sub-Stencils for the Degasperis-Procesi Type Equations  

作　　者：Jianfang Lin Yan Xu Huiwen Xue Xinghui Zhong 

机构地区：[1]School of Mathematical Sciences,Zhejiang University,Hangzhou,Zhejiang 310058,P.R.China [2]School of Mathematical Sciences,University of Science and Technology of China,Hefei,Anhui 230026,P.R.China

出　　处：《Communications in Computational Physics》2022年第3期913-946,共34页计算物理通讯（英文）

基　　金：supported by National Natural Science Foundation of China(Grant No.12071455);supported by National Natural Science Foundation of China(Grant No.11871428)。

摘　　要：In this paper,we develop twofinite difference weighted essentially non-oscillatory(WENO)schemes with unequal-sized sub-stencils for solving the Degasperis-Procesi(DP)andµ-Degasperis-Procesi(µDP)equations,which contain nonlinear high order derivatives,and possibly peakon solutions or shock waves.By introducing auxiliary variable(s),we rewrite the DP equation as a hyperbolic-elliptic system,and theµDP equation as afirst order system.Then we choose a linearfinite difference scheme with suitable order of accuracy for the auxiliary variable(s),and twofinite difference WENO schemes with unequal-sized sub-stencils for the primal variable.One WENO scheme uses one large stencil and several smaller stencils,and the other WENO scheme is based on the multi-resolution framework which uses a se-ries of unequal-sized hierarchical central stencils.Comparing with the classical WENO scheme which uses several small stencils of the same size to make up a big stencil,both WENO schemes with unequal-sized sub-stencils are simple in the choice of the stencil and enjoy the freedom of arbitrary positive linear weights.Another advantage is that thefinal reconstructed polynomial on the target cell is a polynomial of the same de-gree as the polynomial over the big stencil,while the classicalfinite difference WENO reconstruction can only be obtained for specific points inside the target interval.Nu-merical tests are provided to demonstrate the high order accuracy and non-oscillatory properties of the proposed schemes.

关 键 词：High order accuracy weighted essentially non-oscillatory schemes Degasperis-Procesi equation µ-Degasperis-Procesi equation finite difference method MULTI-RESOLUTION 

分 类 号：O17[理学—数学]