-
1
-
-
0015484437
-
Comparing numerical methods for ordinary differential equations
-
T.E. Hull, W.H. Enright, B.M. Fellen and A.E. Sedgwick, Comparing numerical methods for ordinary differential equations, SIAM J. Numer. Anal. 4, 603-637, (1972).
-
(1972)
SIAM J. Numer. Anal.
, vol.4
, pp. 603-637
-
-
Hull, T.E.1
Enright, W.H.2
Fellen, B.M.3
Sedgwick, A.E.4
-
2
-
-
34250486951
-
Klassische Runge-Kutta-Formeln vierter und niedriger ordnung mit schrittweiten-kontrolle und ihre anwendung auf wärmeleitungsprobleme
-
E. Fehlberg, Klassische Runge-Kutta-Formeln vierter und niedriger Ordnung mit Schrittweiten-Kontrolle und ihre Anwendung auf Wärmeleitungsprobleme, Computing 7, 61-71, (1970).
-
(1970)
Computing
, vol.7
, pp. 61-71
-
-
Fehlberg, E.1
-
3
-
-
84968517891
-
Local extrapolation in the solution of ordinary differential equations
-
L.F. Shampine, Local extrapolation in the solution of ordinary differential equations, Math. Comp. 27, 91-97, (1973).
-
(1973)
Math. Comp.
, vol.27
, pp. 91-97
-
-
Shampine, L.F.1
-
4
-
-
0016971912
-
Solving nonstiff ordinary differential equations - The state of the art
-
L.F. Shampine, H.A. Watts and S.M. Davenport, Solving nonstiff ordinary differential equations - The state of the art, SIAM Review 18, 376-411, (1976).
-
(1976)
SIAM Review
, vol.18
, pp. 376-411
-
-
Shampine, L.F.1
Watts, H.A.2
Davenport, S.M.3
-
5
-
-
0018991720
-
A family of embedded Runge-Kutta formulas
-
J.R. Dormand and P.J. Prince, A family of embedded Runge-Kutta formulas, J. Comp. Appl. Math. 6, 19-26, (1980).
-
(1980)
J. Comp. Appl. Math.
, vol.6
, pp. 19-26
-
-
Dormand, J.R.1
Prince, P.J.2
-
6
-
-
84966237458
-
Some practical Runge-Kutta formulas
-
L.F. Shampine, Some practical Runge-Kutta formulas, Math. Comp. 46, 135-150, (1986).
-
(1986)
Math. Comp.
, vol.46
, pp. 135-150
-
-
Shampine, L.F.1
-
7
-
-
0038440068
-
Explicit Runge-Kutta pairs with one more derivative evaluation than the minimum
-
P.W. Sharp and E. Smart, Explicit Runge-Kutta pairs with one more derivative evaluation than the minimum, SIAM J. Sci. Comput. 14, 338-348, (1993).
-
(1993)
SIAM J. Sci. Comput.
, vol.14
, pp. 338-348
-
-
Sharp, P.W.1
Smart, E.2
-
8
-
-
0039638076
-
Fourth- and fifth-order, scaled Runge-Kutta algorithms for treating dense output
-
M.K. Horn, Fourth-and fifth-order, scaled Runge-Kutta algorithms for treating dense output, SIAM J. Numer. Anal. 20, 558-568, (1983).
-
(1983)
SIAM J. Numer. Anal.
, vol.20
, pp. 558-568
-
-
Horn, M.K.1
-
9
-
-
0022784120
-
Interpolants for Runge-Kutta formulas
-
W.H. Enright, K.R. Jackson, S.P. Nørsett and P.G. Thomsen, Interpolants for Runge-Kutta formulas, ACM Trans. Math. Soft. 12, 193-218, (1986).
-
(1986)
ACM Trans. Math. Soft.
, vol.12
, pp. 193-218
-
-
Enright, W.H.1
Jackson, K.R.2
Nørsett, S.P.3
Thomsen, P.G.4
-
10
-
-
0022144651
-
Interpolation for Runge-Kutta methods
-
L.F. Shampine, Interpolation for Runge-Kutta methods, SIAM J. Numer. Anal. 22, 1014-1027, (1985).
-
(1985)
SIAM J. Numer. Anal.
, vol.22
, pp. 1014-1027
-
-
Shampine, L.F.1
-
11
-
-
0043028727
-
Practical aspects of interpolation in Runge-Kutta codes
-
I. Gladwell, L.F. Shampine, L. Baca and R.W. Brankin, Practical aspects of interpolation in Runge-Kutta codes, SIAM J. Sci. Stat. Comput. 8, 322-341, (1987).
-
(1987)
SIAM J. Sci. Stat. Comput.
, vol.8
, pp. 322-341
-
-
Gladwell, I.1
Shampine, L.F.2
Baca, L.3
Brankin, R.W.4
-
13
-
-
30244547380
-
New continuous extensions for the Dormand and Prince RK method
-
Edited by J.R. Cash and I. Gladwell, Clarendon Press, Oxford, U.K.
-
M. Calvo, J.I. Montijano and L. Randez, New continuous extensions for the Dormand and Prince RK method, In Computational Ordinary Differential Equations, (Edited by J.R. Cash and I. Gladwell), pp. 135-144, Clarendon Press, Oxford, U.K., (1992).
-
(1992)
Computational Ordinary Differential Equations
, pp. 135-144
-
-
Calvo, M.1
Montijano, J.I.2
Randez, L.3
-
14
-
-
0005691331
-
Robust defect control with Runge-Kutta schemes
-
D.J. Higham, Robust defect control with Runge-Kutta schemes, SIAM J. Numer. Anal. 26, 1175-1183, (1989).
-
(1989)
SIAM J. Numer. Anal.
, vol.26
, pp. 1175-1183
-
-
Higham, D.J.1
-
15
-
-
0004006811
-
Practical solution of ordinary differential equations by Runge-Kutta methods
-
Sandia National Laboratories, Albuquerque, NM
-
L.F. Shampine and H.A. Watts, Practical solution of ordinary differential equations by Runge-Kutta methods, Rept. SAND 76-0585, Sandia National Laboratories, Albuquerque, NM, (1976).
-
(1976)
Rept. SAND 76-0585
-
-
Shampine, L.F.1
Watts, H.A.2
-
16
-
-
30244479253
-
-
Math. Dept., Southern Methodist University, Dallas, TX
-
G.L. Kraut, A comparison of RKSUITE with Runge-Kutta codes from the NAG, SLATEC, and IMSL libraries, Math. Dept., Southern Methodist University, Dallas, TX, (1991).
-
(1991)
A Comparison of RKSUITE with Runge-Kutta Codes from the NAG, SLATEC, and IMSL Libraries
-
-
Kraut, G.L.1
-
17
-
-
30244491660
-
-
RKSUITE
-
RKSUITE: http://www.netlib.org/ode/rksuite/.
-
-
-
-
18
-
-
0004311269
-
RKSUITE: A suite of Runge-Kutta codes for the initial value problem for ODEs
-
Math. Dept., Southern Methodist University, Dallas, TX
-
R.W. Brankin, I. Gladwell and L.F. Shampine, RKSUITE: A suite of Runge-Kutta codes for the initial value problem for ODEs, Softreport 91-1, Math. Dept., Southern Methodist University, Dallas, TX, (1991).
-
(1991)
Softreport 91-1
-
-
Brankin, R.W.1
Gladwell, I.2
Shampine, L.F.3
-
20
-
-
0004332272
-
-
NAG Ltd., Wilkinson House, Jordanhill Road, Oxford, U.K.
-
NAG Fortran Library Manual, Mark 13, NAG Ltd., Wilkinson House, Jordanhill Road, Oxford, U.K., (1988).
-
(1988)
NAG Fortran Library Manual, Mark 13
-
-
-
21
-
-
0040654719
-
-
IMSL, 2500 Park West Tower One, 2500 City West Boulevard, Houston, TX
-
IMSL Math/Library User's Manual, Version 1.1, IMSL, 2500 Park West Tower One, 2500 City West Boulevard, Houston, TX, (1989).
-
(1989)
IMSL Math/library User's Manual, Version 1.1
-
-
-
22
-
-
30244489766
-
Computation of truncation error terms for runge-kutta methods
-
Tech. Univ. Munich, (private communication)
-
D.G. Bettis and M.K. Horn, Computation of truncation error terms for Runge-Kutta methods, Math. Inst. report, Tech. Univ. Munich, (private communication).
-
Math. Inst. Report
-
-
Bettis, D.G.1
Horn, M.K.2
-
23
-
-
84910273547
-
The quality of Runge-Kutta formulas
-
Sandia National Laboratories, Albuquerque, NM
-
L.F. Shampine, The quality of Runge-Kutta formulas, Rept. SAND 76-0370, Sandia National Laboratories, Albuquerque, NM, (1976).
-
(1976)
Rept. SAND 76-0370
-
-
Shampine, L.F.1
-
25
-
-
49149135749
-
High order embedded Runge-Kutta formulas
-
P.J. Prince and J.R. Dormand, High order embedded Runge-Kutta formulas, J. Comp. Appl. Math. 7, 67-75, (1981).
-
(1981)
J. Comp. Appl. Math.
, vol.7
, pp. 67-75
-
-
Prince, P.J.1
Dormand, J.R.2
-
27
-
-
0020148962
-
Implementation of Rosenbrock methods
-
L.F. Shampine, Implementation of Rosenbrock methods, ACM Trans. Math. Software 8, 93-113, (1982).
-
(1982)
ACM Trans. Math. Software
, vol.8
, pp. 93-113
-
-
Shampine, L.F.1
-
28
-
-
45249130262
-
A 3(2) pair of Runge-Kutta formulas
-
P. Bogacki and L.F. Shampine, A 3(2) pair of Runge-Kutta formulas, Appl. Math. Lett. 2 (4), 1-9, (1989).
-
(1989)
Appl. Math. Lett.
, vol.2
, Issue.4
, pp. 1-9
-
-
Bogacki, P.1
Shampine, L.F.2
-
29
-
-
0024937925
-
Global error estimation with Runge-Kutta triples
-
J.R. Dormand, M.A. Lockyear, N.E. McGorrigan and P.J. Prince, Global error estimation with Runge-Kutta triples, Computers Math. Applic. 18 (9), 835-846, (1989).
-
(1989)
Computers Math. Applic.
, vol.18
, Issue.9
, pp. 835-846
-
-
Dormand, J.R.1
Lockyear, M.A.2
McGorrigan, N.E.3
Prince, P.J.4
-
30
-
-
0039094317
-
-
Ph.D. Thesis, Math. Dept., Southern Methodist University, Dallas, TX
-
P. Bogacki, Efficient Runge-Kutta pairs and their interpolants, Ph.D. Thesis, Math. Dept., Southern Methodist University, Dallas, TX, (1990).
-
(1990)
Efficient Runge-Kutta Pairs and Their Interpolants
-
-
Bogacki, P.1
-
31
-
-
0345781788
-
-
Rept. 89-20, Math. Dept., Southern Methodist University, Dallas, TX
-
P. Bogacki and L.F. Shampine, An efficient Runge-Kutta (4,5) pair, Rept. 89-20, Math. Dept., Southern Methodist University, Dallas, TX, (1989).
-
(1989)
An Efficient Runge-Kutta (4,5) Pair
-
-
Bogacki, P.1
Shampine, L.F.2
-
33
-
-
30244559251
-
The SLATEC common mathematical library, chapter 11
-
(Edited by W.R. Cowell), Prentice Hall, Englewood Cliffs, NJ
-
B.L. Buzbee, The SLATEC common mathematical library, Chapter 11, In Sources and Development of Mathematical Software, (Edited by W.R. Cowell), Prentice Hall, Englewood Cliffs, NJ, (1984).
-
(1984)
Sources and Development of Mathematical Software
-
-
Buzbee, B.L.1
-
34
-
-
0016443950
-
Comparing numerical methods for stiff systems for O.D.E.'s
-
W.H. Enright, T.E. Hull and B. Lindberg, Comparing numerical methods for stiff systems for O.D.E.'s, BIT 15, 10-48, (1975).
-
(1975)
BIT
, vol.15
, pp. 10-48
-
-
Enright, W.H.1
Hull, T.E.2
Lindberg, B.3
|