Numerical implementation of the multisymplectic Preissman scheme and its equivalent schemes

doi:10.1016/S0096-3003(03)00080-8

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	Numerical implementation of the multisymplectic Preissman scheme and its equivalent schemes
	Wang, YS ; Wang, B ; Qin, MZ
	2004-02-12
发表期刊	APPLIED MATHEMATICS AND COMPUTATION
ISSN	0096-3003
卷号	149 期号:2 页码:299-326
摘要	We analyze the multisymplectic Preissman scheme for the KdV equation with the periodic boundary condition and show that the unconvergence of the widely used iterative methods to solve the resulting nonlinear algebra system of the Preissman scheme is due to the introduced potential function. A artificial numerical condition is added to the periodic boundary condition. The added boundary condition makes the numerical implementation of the multisymplectic Preissman scheme practical and is proved not to change the numerical solutions of the KdV equation. Based on our analysis, we derive some new schemes which are not restricted by the artificial boundary condition and more efficient than the Preissman scheme because of less computing cost and less computer storages. By eliminating the auxiliary variables, we also derive two schemes for the KdV equation, one is a 12-point scheme and the other is an 8-point scheme. As the byproducts, we present two new explicit schemes which are not multisymplectic but still have remarkable numerical stable property. Numerical experiments on soliton collisions are also provided to confirm our conclusion and to show the benefits of the multisymplectic schemes with comparison of the spectral method and Zabusky-Kruskal scheme. (C) 2003 Elsevier Inc. All rights reserved.
DOI	10.1016/S0096-3003(03)00080-8
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000188651000001
出版者	ELSEVIER SCIENCE INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/19149
专题	中国科学院数学与系统科学研究院
通讯作者	Wang, YS
作者单位	1.Chinese Acad Sci, Inst Atmospher Phys, LASG, Beijing 100029, Peoples R China 2.Chinese Acad Sci, Sch Math & Syst Sci, LSEC, Beijing 100080, Peoples R China 3.Nanjing Normal Univ, Dept Math, Nanjing 210097, Peoples R China
推荐引用方式 GB/T 7714	Wang, YS,Wang, B,Qin, MZ. Numerical implementation of the multisymplectic Preissman scheme and its equivalent schemes[J]. APPLIED MATHEMATICS AND COMPUTATION,2004,149(2):299-326.
APA	Wang, YS,Wang, B,&Qin, MZ.(2004).Numerical implementation of the multisymplectic Preissman scheme and its equivalent schemes.APPLIED MATHEMATICS AND COMPUTATION,149(2),299-326.
MLA	Wang, YS,et al."Numerical implementation of the multisymplectic Preissman scheme and its equivalent schemes".APPLIED MATHEMATICS AND COMPUTATION 149.2(2004):299-326.