A Splitting Method for the Degasperis-Procesi Equation Using an Optimized WENO Scheme and the Fourier Pseudospectral Method

作     者：Yunrui Guo Wenjing Yang Hong Zhang Ji Wang Songhe Song 

作者机构：State Key Laboratory of High Performance ComputingCollege of ComputerNational University of Defense TechnologyChangsha 410073China Department of MathematicsUtrecht UniversityThe Netherlands P.O.Box 80.0103508TAUtrecht Department of MathematicsCollege of SciencesNational University of Defense TechnologyChangsha 410073China 

出 版 物：《Advances in Applied Mathematics and Mechanics》 (应用数学与力学进展（英文）)

年 卷 期：2019年第11卷第1期

页      面：53-71页

核心收录：

学科分类：07[理学] 0802[工学-机械工程] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 

基　　金：This work was supported by National Natural Science Foundation of China(Grant No.91648204) National Key Research and Development Program of China(Grant No.2016YFB0201301) Science Challenge Project(Nos.JCKY2016212A502,TZ2016002). 

主　　题：Degasperis-Procesi equation discontinuous solution weighted essentially nonoscillatory method pseudospectral method 

摘      要：The Degasperis-Procesi(DP)equation is split into a system of a hyperbolic equation and an elliptic equation.For the hyperbolic equation,we use an optimized finite difference weighted essentially non-oscillatory(OWENO)scheme.New smoothness measurement is presented to approximate the typical shockpeakon structure in the solution to the DP equation,which evidently reduces the dissipation arising from discontinuities simultaneously removing nonphysical oscillations.For the elliptic equation,the Fourier pseudospectral method(FPM)is employed to discretize the high order derivative.Due to the combination of the WENO reconstruction and FPM,the splitting method shows an excellent performance in capturing the formation and propagation of shockpeakon solutions.The numerical simulations for different solutions of the DP equation are conducted to illustrate the high accuracy and capability of the method.