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Runge-Kutta-Nystrm方法的若干新性质

陈全发,肖爱国,   

  1. 湘南学院数学系,湘潭大学数学与计算科学学院 湖南郴州423000,湖南湘潭411105
  • 出版日期:2008-02-14 发布日期:2008-02-14

陈全发,肖爱国,. Runge-Kutta-Nystrm方法的若干新性质[J]. 计算数学, 2008, 30(2): 201-212.

SOME NEW PROPERTIES OF RUNGE-KUTTA-NYSTRM METHODS

  1. Chen Quanfa (Department of Mathematics,Xiangnan University,Chenzhou 423000,China) Xiao Aiguo (School of Mathematics and Computational Science,Xiangtan University,Xiangtan 411105,China)
  • Online:2008-02-14 Published:2008-02-14
本文研究了由Runge-Kutta(RK)方法Φ生成Runge-Kutta-Nystr(?)m(RKN)方法Φ_N的伴随西Φ~*_N的两种途径,证明了由这两条途径生成的西Φ~*_N是相同的;讨论了具有辛性,对称性或P-稳定性的Φ,Φ_N,Φ~*_N之间的一些关系;并表明通过辛(或对称)RK方法可构造辛(或对称) RKN方法.
In this paper,two different approaches to generating the adjoint methodΦ~*_N of a Runge- Kutta-NystrSm (RKN) methodΦ_N from a Runge-Kutta (RK) methodΦare studied,and it is shown that these two approaches generate the sameΦ~*_N.The relations among symplecticity, symmetry and P-stability ofΦ,Φ_N andΦ~*_N are also discussed.An approach to constructing symplectic (or symmetric) RKN methods from symplectic (or symmetric) RK methods is presented.
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