Computation of the interval of stability of Runge-Kutta-Nyström methods

Journal of Symbolic Computation

Volumn 25, Issue 3, 1998, Pages 383-394

  Paternoster, B ^a   Cafaro, M ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032019937     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsco.1997.0183     Document Type: Article

References (19)

1. Brankin, R.W., Gladwell, I., Dormand, J.R., Prince, P.J. (1989). ALGORITHM 670, A Runge-Kutta Nystroöm Code. ACM Trans. Math. Software 15(1), 31-40.
2. Calvo, M.P. (1991). Metodos Runge-Kutta-Nyström simplecticos. Ph.D. Thesis, University of Valladolid.
3. Crisci, M.R., Paternoster, B., Russo, E. (1993). Fully parallel Runge-Kutta Nyström methods for ODES with oscillating solutions. Appl. Numer. Math. 11, 143-158.
4. Dekker, K., Verwer, J.G. (1984). Stability of Runge-Kutta methods for stiff nonlinear differential equations, CWI Monograph, North-Holland, Amsterdam.
5. Dormand, J.R., El-Mikkawy, M.E.A., Prince, P.J. (1987a) I. Families of Runge-Kutta-Nyström formulae. IMA J. Num. Anal. 7, 235-250.
6. Dormand, J.R., El-Mikkawy, M.E.A., Prince, P.J. (1987b) II. High-order embedded Runge-Kutta-Nyström formulae. IMA J. Num. Anal. 7, 423-430.
7. Dormand, J.R., Prince, P.J. (1988). New Runge-Kutta-Nyström triples. Comput. Math. Applic. 14, 1007-1017.
8. Filippi, S., Gräf, J. (1986). New Runge-Kutta-Nyström formula-pairs of order 8(7), 9(8), 10(9) and 11(10) for differential equations of the form y″ = f(x, y). J. Comput. Appl. Math. 14, 361-370.
9. Hairer, E. (1979). Unconditionally stable methods for second-order differential equations. Numer. Math. 32, 373-379.
10. Hairer, E. (1982). A one-step method of order 10 for y″ = f(x, y). IMA J. Num. Anal. 2, 83-94.
11. Hairer, E., Norsett, S.P., Wanner, G. (1987). Solving ordinary differential equations I - Nonstiff problems. Springer Series in Computational Mathematics 8, Springer, Berlin.
12. Lambert, J.D. (1991). Numerical Methods for Ordinary Differential Systems - The Initial Value Problem. John Wiley & Sons.
13. Okunbor, D.I., Skeel, R.D. (1994). Canonical Runge-Kutta-Nyström methods of orders five and six. J. Comput. Appl. Math. 51, 375-382.
14. Sharp, P.W., Fine, J.M., Burrage, K. (1990). Two-stage and three-stage diagonally implicit Runge-Kutta Nyström methods of orders three and four. IMA J. Num. Anal. 10, 489-504.
15. Sofroniou, M. (1994). Symbolic derivation of Runge-Kutta methods, J. Symbol. Comput. 18 (3), 265-296.
16. Van der Houwen, P.J. (1979). Stabilized Runge-Kutta methods for second order differential equaions without first derivatives. SIAM J. Num. Anal. 16, 523-537.
17. Van der Houwen, P.J., Sommeijer, B.P. (1989). Diagonally implicit Runge-Kutta Nyström methods for oscillatory problems. SIAM J. Num. Anal. 26, 414-429.
18. Van der Houwen, P.J., Sommeijer, B.P., Nhuyen Huu Cong (1991). Stability of collocation-based Runge-Kutta-Nyström methods. BIT 31, 469-481.
19. Wolfram, S. (1991). Mathematica, A System for Doing Mathematics by Computer. Addison Wesley.