High-order embedded runge-kutta-nystrom formulae

IMA Journal of Numerical Analysis

Volumn 7, Issue 4, 1987, Pages 423-430

  Dormand, J R ^a   El mikkawy, M E A ^a   Prince, P J ^a  

^a TEESSIDE UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77957212547     PISSN: 02724979     EISSN: None     Source Type: Journal    
DOI: 10.1093/imanum/7.4.423     Document Type: Article

References (8)

1. Dormand, J. R., & Prince, P. J. 1978 New Runge-Kutta-Nystrom algorithms for simulation in dynamical astronomy. Celestial Mechanics 18, 223-232.
2. Dormand, J. R., El-Mikkawy, M. E. A., & Prince, P. J. 1987 Families of Runge-Kutta-Nystron formulae. To appear in IMA J. Num. Analysis.
3. El-Mikkawy, M. E. A. 1986 Embedded Runge-Kutta-Nystrom methods. Ph.D. Thesis, CNAA.
4. Fehlberg, E. 1972 Classical eighth and lower order Runge-Kutta-Nystrom formulas with step size control for special second order differential equations. NASA TR 238-381.
5. Filippi, S., & Graf, J. 1986 New Runge-Kutta-Nystrom 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. Maths. 14, 361-370.
6. Hairer, E. 1982 A one-step method of order 10 for y" = f(x, y). IMA J. Num. Analysis 2, 83-94.
7. Horn, M. K. 1977 Developments in high order Runge-Kutta-Nystrom formulas. Dissertation: The University of Texas at Austin.
8. Prince, P. J. 1979 Runge-Kutta processes with global error estimation. Ph.D. Thesis, CNAA.