Gauss-Runge-Kutta-Nystrom methods

BIT Numerical Mathematics

Volumn 38, Issue 1, 1998, Pages 12-21

  Burnton, Christopher ^b   Scherer, Rudolf ^a  

^a UNIVERSITY OF KARLSRUHE   (Germany)

^b NONE

Author keywords

Gauss method; Hamiltonian system; Runge Kutta Nystr m method; Symplectic method

Indexed keywords

EID: 0348229165     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02510913     Document Type: Article

References (12)

1. V. I. Arnold, Mathematical Methods of Classical Mechanics, 2nd Edition, Springer, New York, 1989.
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3. J. C. Butcher, The Numerical Analysis of Ordinary Differential Equations, John Wiley, Chichester, 1987.
4. M. P. Calvo and J. M. Sanz-Serna, Order conditions for canonical Runge-Kutta-Nyström methods, BIT, 32 (1992), pp. 131-142.
5. P. Görtz and R. Scherer, Reducibility and characterization of symplectic Runge-Kutta methods, ETNA, 2 (1994), pp. 194-204.
6. E. Hairer, S. P. Nørsett, and G. Wanner, Solving Ordinary Differential Equations I, Nonstiff Systems, Springer, Berlin, 1987.
7. E. Hairer and G. Wanner, A theory for Nystrom methods, Numer. Math., 25 (1976), pp. 383-400.
8. E. Hairer, Méthodes de Nyström pour l'équation différentielle y″ = f(x,y), Numer. Math., 27 (1977), pp. 283-300.
9. D. Okunbor and R. D. Skeel, An explicit Runge-Kutta-Nyström method is canonical if and only if its adjoint is explicit, SIAM J. Numer. Anal., 29 (1992), pp. 521-527.
10. M.-Z. Qin and W.-J. Zhu, Canonical Runge-Kutta-Nyström methods for second order ordinary differential equations, Computers Math. Applic., 22 (1991), pp. 85-95.
11. J. M. Sanz-Serna, Runge-Kutta schemes for Hamiltonian systems, BIT, 28 (1988), pp. 877-883.
12. J. M. Sanz-Serna and M. P. Calvo, Numerical Hamiltonian Problems, Chapman and Hall, London 1994.