From: spellucci@mathematik.tu-darmstadt.de (Peter Spellucci)
Subject: Re: Runge-Kutta method by Dormand and Prince
Date: 18 Sep 2000 13:45:40 GMT
Newsgroups: sci.math.num-analysis
Summary: [missing]

In article <8q09u5$bej$1@nslave2.tin.it>,
 "Michael Knaus" <knaMi@remnet.com> writes:
|> Where I can find an exhaustive explanation  about ODE Runge-Kutta method by
|> Dormand and Prince?
|> 
|> 
I suppose you mean the 4/5 pair from the early eighties? 
there is lot of information in

hairer & norsett & wanner ; solving ordinary differential equations I 
(springer ) 
but there has been much development in this filed since then:
Dormand, J.R.; Prince, P.J.
A family of embedded Runge-Kutta formulae. (English)
[J] J. Comput. Appl. Math. 6, 19-26 (1980).

449.65048
Prince, P.J.; Dormand, J.R.
High order embedded Runge-Kutta formulae. (German)
[J] J. Comput. Appl. Math. 7, 67-75 (1981).

Dormand, J.R.; Duckers, R.R.; Prince, P.J.
Global error estimation with Runge-Kutta methods. (English)
[J] IMA J. Numer. Anal. 4, 169-184 (1984).

Dormand, J.R.; Prince, P.J.
Global error estimation with Runge-Kutta methods. II. (English)
[J] IMA J. Numer. Anal. 5, 481-497 (1985).

618.65059 
Dormand, J.R.; Prince, P.J.
Runge-Kutta triples. (English)
[J] Comput. Math. Appl., Part A 12, 1007-1017 (1986).

Dormand, J.R.; El-Mikkawy, M.E.A.; Prince, P.J.
Families of Runge-Kutta-Nystroem formulae. (English)
[J] IMA J. Numer. Anal. 7, 235-250 (1987).

Dormand, J.R.; Prince, P.J.
Runge-Kutta-Nystroem triples. (English)
[J] Comput. Math. Appl. 13, 937-949 (1987).


Brankin, R.W.; Gladwell, I.; Dormand, J.R.; Prince, P.J.; Seward, W.L.
A Runge-Kutta-Nystroem code. (English)
[J] ACM Trans. Math. Software 15, No.1, 31-40 (1989).


Dormand, J.R.; Lockyer, M.A.; McGorrigan, N.E.; Prince, P.J.
Global error estimation with Runge-Kutta triples. (English)
[J] Comput. Math. Appl. 18, No.9, 835-846 (1989).

Dormand, J.R.; Prince, P.J.
Practical Runge-Kutta processes. (English)
[J] SIAM J. Sci. Stat. Comput. 10, No.5, 977-989 (1989).



Dormand, J.R.; Gilmore, J.P.; Prince, P.J.
Globally embedded Runge-Kutta schemes. (English)
[J] Ann. Numer. Math. 1, No.1-4, 97-106 (1994).


Baker, T.S.; Dormand, J.R.; Gilmore, J.P.; Prince, P.J.
Continuous approximation with embedded Runge-Kutta methods. (English)
[J] Appl. Numer. Math. 22, No.1-3, 51-62 (1996). [ISSN 0168-9274]

Baker, T.S.; Dormand, J.R.; Prince, P.J.
Continuous approximation with embedded Runge-Kutta-Nystroem methods. (English)
[J] Appl. Numer. Math. 29, No.2, 171-188 (1999). [ISSN 0168-9274] http://www.elsevier.nl/locate/apnum/


and this one :


Bogacki, P.; Shampine, L.F.
An efficient Runge-Kutta $(4,5)$ pair. (English)
[J] Comput. Math. Appl. 32, No.6, 15-28 (1996). [ISSN 0097-4943]
A pair of explicit Runge-Kutta formulas of orders 4 and 5 is derived. 
It is significantly more efficient than the Fehlberg and Dormand-Prince pairs, 
and by
standard measures it is of at least as high quality. There are two 
independent estimates of the local error. The local error of the 
interpolant is, to leading
order, a problem-independent function of the local error at the end of the step.


hope this helps
peter