Algorithm 670: a Runge-Kutta-Nyström code

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Algorithm 670: a Runge-Kutta-Nyström code

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 15 , Issue 1 (March 1989) table of contents

Pages: 31 - 40

Year of Publication: 1989

ISSN:0098-3500

Authors

R. W. Brankin	Numerical Algorithms Group Ltd., Oxford, England, UK
I. Gladwell	Southern Methodist Univ., Dallas, TX
J. R. Dormand	Teesside Polytechnic, Middlesbrough, England, UK
P. J. Prince	Teesside Polytechnic, Middlesbrough, England, UK
W. L. Seward	Univ. of Waterloo, Waterloo, Ont., Canada

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ACM New York, NY, USA

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Downloads (6 Weeks): 13, Downloads (12 Months): 139, Citation Count: 2

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appendices and supplements references cited by index terms collaborative colleagues

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APPENDICES and SUPPLEMENTS

670.gz (40 KB)

Runge-Kutta-Nystrom. Two embedded formula pairs are provided, the lower order pair allowing interpolation
Gams: I1a1a

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	BRANKIN, R. W., DORMAND, J. R., GLADWELL, I., PRINCE, P. J., AND SEWARD, W. A Runge- Kutta-Nystr6m Code. Num. Anal. Rep. 136, University of Manchester, Manchester, England, 1987.
	2	DORMAND, J. R., AND PRINCE, P.J. New Runge-Kutta-Nystr6m algorithms for simulation in dynamical astronomy. Celestial Mechanics 18 (1978), 223-232.
	3	DORMAND, J. R., AND PRINCE, P.J. Runge-Kutta-Nystrbm triples. Comp. and Math. with Appl. 14 (1988), 1007-1017.
	4	DORMAND, J. R., EL-MIKKAWY, M. E. A., AND PRINCE, P.J. Families of Runge-Kutta-Nystr6m formulae. IMA J. Numer. Anal. 7 (1987), 235-250.
	5	DORMAND, J. R., EL-MIKKAWY, M. E. A., AND PRINCE, P.Z. High order embedded Runge- Kutta-NystrSm formulae. IMA J. Nurner. Anal. 7 (1987), 423-430.
	6	W. H. Enright , K. R. Jackson , S. P. Nørsett , P. G. Thomsen, Interpolants for Runge-Kutta formulas, ACM Transactions on Mathematical Software (TOMS), v.12 n.3, p.193-218, Sept. 1986 [doi>10.1145/7921.7923]
	7	FEHLBERG, E. Classical eighth and lower order Runge-Kutta-Nystr6m formulas with step size control for special second order differential equations. NASA Tech. Rep. R-381, Washington, D.C., 1972.
	8	S Philippi , J Gräf, New Runge-Jutta-Nystrom formula-pairs of order 8(7), 9(8), 10(9) and 11(10) for differential equations of the form y" = f(x,y), Journal of Computational and Applied Mathematics, v.14 n.3, p.361-370, March 1986 [doi>10.1016/0377-0427(86)90073-7]
	9	Ian Gladwell, Initial Value Routines in the NAG Library, ACM Transactions on Mathematical Software (TOMS), v.5 n.4, p.386-400, Dec. 1979 [doi>10.1145/355853.355856]
	10	M. Berzins , R. W. Brankin , I. Gladwell, The stiff integrators in the NAG library, ACM SIGNUM Newsletter, v.23 n.2, p.16-23, April 1988 [doi>10.1145/47917.47921]
	11	I. Gladwell , L. F. Shampine , R. W. Brankin, Automatic selection of the initial step size for an ODE solver, Journal of Computational and Applied Mathematics, v.18 n.2, p.175-192, May 1987 [doi>10.1016/0377-0427(87)90015-X]
	12	GLADWELL, I., SHAMPINE, L. F., AND BRANKIN, R.W. Locating special events when solving ODEs. Appl. Math. Lett. 1 (1988), 153-156.
	13	I. Gladwell , L. F. Shampine , L. S. Baca , R. W. Brankin, Practical aspects of interpolation in Runge-Kutta codes, SIAM Journal on Scientific and Statistical Computing, v.8 n.3, p.322-341, May 1, 1987 [doi>10.1137/0908038]
	14	HAIRER, E. M~thodes de Nystr6m pour l'~quation differentielle y" = f(x, y). Numer. Math. 27 (1977), 283-300.
	15	HORN, M.K. Fourth- and fifth-order, scaled Runge-Kutta algorithms for treating dense output. SIAM J. Numer. Anal. 20 (1983) 558-568.
	16	ISTPF, Toolpack/1 Release 2.1, PFORT-77 portability verifier. NAG Publication NP1312, Numerical Algorithms Group Ltd., Oxford, England.
	17	L. F. Shampine, Storage Reduction for Runge-Kutta Codes, ACM Transactions on Mathematical Software (TOMS), v.5 n.3, p.245-250, Sept. 1979 [doi>10.1145/355841.355842]
	18	SHAMPINE, L.F. Interpolation for Runge-Kutta methods. SIAM J. Numer. Anal. 22 (1985), 1014-1027.
	19	Lawrence,F Shampine, Some practical Runge-Kutta formulas, Mathematics of Computation, v.46 n.173, p.135-150, Jan. 1986 [doi>10.2307/2008219]
	20	SHAMPINE, L. F., AND WATTS, H.A. The art of writing a Runge-Kutta code, Part I. Mathematical Software III, J. R. Rice, Ed. Academic Press, Orlando, Fla., 1977, 257-275.
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	22	SHAMPINE, L. F., AND WATTS, H.A. DEPAC--Design of a user-oriented package of ODE solvers. Tech. Rep. SAND79-2374, Sandia National Laboratories, Albuquerque, N. Mex.
	23	VAST VERSION 1.22W. Pacific-Sierra Research, Mill Valley, Calif.

CITED BY 2

	C. A. Addison , W. H. Enright , P. W. Gaffney , I. Gladwell , P. M. Hanson, Algorithm 687: a decision tree for the numerical solution of initial value ordinary differential equations, ACM Transactions on Mathematical Software (TOMS), v.17 n.1, p.1-10, March 1991
	Philip W. Sharp, N-body simulations: The performance of some integrators, ACM Transactions on Mathematical Software (TOMS), v.32 n.3, p.375-395, September 2006