Symmetric-Adjoint and Symplectic-Adjoint Runge-Kutta Methods and Their Applications

doi:10.4208/nmtma.OA-2021-0097

CSpace

	Symmetric-Adjoint and Symplectic-Adjoint Runge-Kutta Methods and Their Applications
	Sun, Geng 1; Gan, Siqing 2; Liu, Hongyu 3; Shang, Zaijiu 1
	2022-02-17
发表期刊	NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS
ISSN	1004-8979
页码	32
摘要	Symmetric and symplectic methods are classical notions in the theory of numerical methods for solving ordinary differential equations. They can generate numerical flows that respectively preserve the symmetry and symplecticity of the continuous flows in the phase space. This article is mainly concerned with the symmetric-adjoint and symplectic-adjoint Runge-Kutta methods as well as their applications. It is a continuation and an extension of the study in [14], where the authors introduced the notion of symplectic-adjoint method of a Runge-Kutta method and provided a simple way to construct symplectic partitioned Runge-Kutta methods via the symplectic-adjoint method. In this paper, we provide a more comprehensive and systematic study on the properties of the symmetric-adjoint and symplecticadjoint Runge-Kutta methods. These properties reveal some intrinsic connections among some classical Runge-Kutta methods. Moreover, those properties can be used to significantly simplify the order conditions and hence can be applied to the construction of high-order Runge-Kutta methods. As a specific and illustrating application, we construct a novel class of explicit Runge-Kutta methods of stage 6 and order 5. Finally, with the help of symplectic-adjoint method, we thereby obtain a new simple proof of the nonexistence of explicit Runge-Kutta method with stage 5 and order 5.
关键词	Key words Runge-Kutta method symmetric symplectic adjoint high-order explicit method
DOI	10.4208/nmtma.OA-2021-0097
收录类别	SCI
语种	英语
资助项目	NSF of China[11671392] ; NSF of China[11771436] ; NSF of China[11971488] ; Hong Kong RGC General Research Funds[12301218] ; Hong Kong RGC General Research Funds[12302919] ; Hong Kong RGC General Research Funds[12301420]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000756662600001
出版者	GLOBAL SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/60036
专题	中国科学院数学与系统科学研究院
通讯作者	Gan, Siqing
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Cent South Univ, HNP LAMA, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China 3.City Univ Hong Kong, Dept Math, Hong Kong, Peoples R China
推荐引用方式 GB/T 7714	Sun, Geng,Gan, Siqing,Liu, Hongyu,et al. Symmetric-Adjoint and Symplectic-Adjoint Runge-Kutta Methods and Their Applications[J]. NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS,2022:32.
APA	Sun, Geng,Gan, Siqing,Liu, Hongyu,&Shang, Zaijiu.(2022).Symmetric-Adjoint and Symplectic-Adjoint Runge-Kutta Methods and Their Applications.NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS,32.
MLA	Sun, Geng,et al."Symmetric-Adjoint and Symplectic-Adjoint Runge-Kutta Methods and Their Applications".NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS (2022):32.