Multi-symplectic Runge-Kutta methods for nonlinear dirac equations

doi:10.1016/j.jcp.2005.06.001

	Multi-symplectic Runge-Kutta methods for nonlinear dirac equations
	Hong, JL; Li, C
	2006-01-20
发表期刊	JOURNAL OF COMPUTATIONAL PHYSICS
ISSN	0021-9991
卷号	211 期号:2 页码:448-472
摘要	In this paper, we consider the multi-symplectic Runge-Kutta (MSRK) methods applied to the nonlinear Dirac equation in relativistic quantum physics, based on a discovery of the multi-symplecticity of the equation. In particular, the conservation of energy, momentum and charge under MSRK discretizations is investigated by means of numerical experiments and numerical comparisons with non-MSRK methods. Numerical experiments presented reveal that MSRK methods applied to the nonlinear Dirac equation preserve exactly conservation laws of charge and momentum, and conserve the energy conservation in the corresponding numerical accuracy to the method utilized. It is verified numerically that MSRK methods are stable and convergent with respect to the conservation laws of energy, momentum and charge, and MSRK methods preserve not only the inner geometric structure of the equation, but also some crucial conservative properties in quantum physics. A remarkable advantage of MSRK methods applied to the nonlinear Dirac equation is the precise preservation of charge conservation law. (c) 2005 Elsevier Inc. All rights reserved.
关键词	multi-symplectic Runge-Kutta methods conservation laws nonlinear dirac equations
DOI	10.1016/j.jcp.2005.06.001
语种	英语
WOS研究方向	Computer Science ; Physics
WOS类目	Computer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS记录号	WOS:000232736800004
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/3165
专题	计算数学与科学工程计算研究所
通讯作者	Hong, JL
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci & Engn Comp, Beijing 100080, Peoples R China 2.Chinese Acad Sci, Grad Sch, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Hong, JL,Li, C. Multi-symplectic Runge-Kutta methods for nonlinear dirac equations[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2006,211(2):448-472.
APA	Hong, JL,&Li, C.(2006).Multi-symplectic Runge-Kutta methods for nonlinear dirac equations.JOURNAL OF COMPUTATIONAL PHYSICS,211(2),448-472.
MLA	Hong, JL,et al."Multi-symplectic Runge-Kutta methods for nonlinear dirac equations".JOURNAL OF COMPUTATIONAL PHYSICS 211.2(2006):448-472.