Explicit symplectic multidimensional exponential fitting modified Runge-Kutta-Nyström methods
نویسندگان
چکیده
This paper is concerned with multidimensional exponential fitting modified Runge-Kutta-Nyström (MEFMRKN) methods for the system of oscillatory second-order differential equations q ′′(t) +Mq(t) = f (q(t)), where M is a d × d symmetric and positive semi-definite matrix and f (q) is the negative gradient of a potential scalar U(q). We formulate MEFMRKN methods and show clearly the relationship between MEFMRKN methods and multidimensional extended Runge-Kutta-Nyström (ERKN) methods proposed by Wu et al. (Comput. Phys. Comm. 181:1955–1962, 2010). Taking into account the fact that the oscillatory system is a separable Hamiltonian system with Hamiltonian H(p,q) = 2p p + 1 2q Mq + U(q), we derive the symplecticity conditions for the MEFMRKN methCommunicated by Christian Lubich. The research of Xinyuan Wu was supported in part by the Natural Science Foundation of China under Grant 10771099, by the Specialized Research Foundation for the Doctoral Program of Higher Education under Grant 20100091110033, by the 985 Project at Nanjing University under Grant 9112020301 and by A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions. The research of Jianlin Xia was supported in part by NSF grants DMS-1115572 and CHE-0957024. X. Wu · B. Wang Department of Mathematics, Nanjing University, Nanjing 210093, P.R. China X. Wu e-mail: [email protected] B. Wang e-mail: [email protected] X. Wu · B. Wang State Key Laboratory for Novel Software Technology, Nanjing University, Nanjing 210093, P.R. China J. Xia ( ) Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA e-mail: [email protected]
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