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

文献类型：期刊论文

作者Sun, Geng1; Gan, Siqing2; Liu, Hongyu3; Shang, Zaijiu1
刊名NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS
出版日期2022-02-17
页码32
ISSN号1004-8979
关键词Key words Runge-Kutta method symmetric symplectic adjoint high-order explicit method
DOI10.4208/nmtma.OA-2021-0097
英文摘要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.
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
语种英语
出版者GLOBAL SCIENCE PRESS
WOS记录号WOS:000756662600001
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/60035]  
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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