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

查看全文 作　　者：Yunrui [1]Guo;Wenjing [1]Yang;Hong [2]Zhang;Ji [1]Wang;Songhe [3]Song 机构地区：[1]State Key Laboratory of High Performance Computing,College of Computer,National University of Defense Technology,Changsha 410073,China;[2]Department of Mathematics,Utrecht University,The Netherlands P.O.Box 80.010,3508TA,Utrecht;[3]Department of Mathematics,College of Sciences,National University of Defense Technology,Changsha 410073,China 出　　处：《Advances in Applied Mathematics and Mechanics》索引2019年第11卷第1期,共19页 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). 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. 关 键 词：Degasperis-Procesi equation discontinuous solution weighted essentially nonoscillatory method pseudospectral method