THE STRUCTURE-PRESERVING METHODS FOR THE DEGASPERIS-PROCESI EQUATION  

作　　者：Yuze Zhang Yushun Wang Yanhong Yang 

机构地区：[1]Department of Applied Mathematics, The Hongkong Polytechnic University, China [2]Jiangsu Key Laboratory of NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China [3]Department of Mathematics, College of Taizhou, Nanjing Normal University, Taizhou 225300, China

出　　处：《Journal of Computational Mathematics》2019年第4期475-487,共13页计算数学（英文）

基　　金：the National Natural Science Foundation of China (Grant No. 11771213);the National Key Research and Development Project of China (Grant No. 2016YFC0600310);the Major Projects of Natural Sciences of University in Jiangsu Province of China (Grant No. 15KJA110002).

摘　　要：This paper gives several structure-preserving schemes for the Degasperis-Procesi equation which has bi-Hamiltonian structures consisted of both complex and non-local Hamiltonian differential operators. For this sake, few structure-preserving schemes have been proposed so far. In our work, based on one of the bi-Hamiltonian structures, a symplectic scheme and two new energy-preserving schemes are constructed. The symplecticity comes straightly from the application of the implicit midpoint method on the semi-discrete system which is proved to remain Hamiltonian, while the energy conservation is derived by the combination of the averaged vector field method of second and fourth order, respectively. Some numerical results are presented to show that the three schemes do have the advantages in numerical stability, accuracy in long time computing and ability to preserve the invariants of the DP equation.

关 键 词：DEGASPERIS-PROCESI EQUATION bi-Hamiltonian structure Structure-preserving SCHEME FOURIER PSEUDOSPECTRAL method 

分 类 号：O1[理学—数学]