%0 Journal Article
%T THE COMPLETE CONSTRUCTION OF FOURTH ORDER SYMPLECTIC EXPLICIT R-K-N METHODS OF THREE STAGES<br>三级四阶显式辛R-K-N格式的完全构造
%A XU Song
%A <br>徐松
%A 侯晓荣
%J 系统科学与数学
%D 2009
%I 
%X The sufficient and necessary conditions for a $p$-th order symmetric Runge-Kutta-Nystr\"om (R-K-N) method of s stages were expressed by a system of nonlinear equations. Thus the construction problem of symmetric schemes is transformed into the problem of solving the system. Under some special conditions, two solutions of the system for s=3 and p=4 were presented, so two fourth order symmetric explicit schemes of three stages were given. Based on Wu's method, we obtain all the solutions of the system for s=3 and p=4 by using Maple software and the software package wsolve in this paper, that is, we construct all the fourth order symplectic explicit R-K-N schemes of three stages. Moreover, we prove that the conditions for a fourth order symmetric explicit R-K-N method of three stages are redundant. Numerical results on the two-body problem indicate the higher precision of the new schemes compared to some existing schemes.
%K Symplectic scheme
%K R-K-N methods
%K complete construction
%K Wu's method<br>辛格式
%K R-K-N方法
%K 完全构造
%K 吴方法.
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=0CD45CC5E994895A7F41A783D4235EC2&aid=E7C6D234FEDF67EBF1F327901D8968F6&yid=DE12191FBD62783C&vid=771469D9D58C34FF&iid=9CF7A0430CBB2DFD&sid=C4B40BDE3E33484C&eid=EC37857E7CB2811A&journal_id=1000-0577&journal_name=系统科学与数学&referenced_num=0&reference_num=9