Multiple order double output Runge-Kutta Fehlberg formulae:
strategies for efficient application
Fredebeul, C.; Kornmaier, D.; Muller, M. W.
Journal of Computational and Applied Mathematics, 2002, vol. 144,
no. 1-2, pp. 187-196, Ingenta.
A fourth order embedded Runge-Kutta RKACeM (4,4) method based
on arithmetic and centroidal means with error
control.
Murugesan, K.; Dhayabaran, D. Paul; Amirtharaj, E. C. Henry;
Evans, David J.
Int. J. Comput.
Math. 79 (2002), no. 2, 247--269,
MathSciNet.
High-order Runge-Kutta-Nyström geometric methods with
processing.
Blanes, S.; Casas, F.; Ros, J.
Special issue: Themes in geometric integration. Appl. Numer. Math.
39 (2001), no. 3-4, 245--259, MathSciNet.
Construction of a five-step singly diagonally implicit
Runge-Kutta-Nyström method and application to the solution of
some problems in elastodynamics. (Spanish)
Franco, J. M.; Gómez, I.
Actes des VI Journées Zaragoza-Pau de
Mathématiques Appliquées et de Statistiques (Jaca,
1999), 241--248, Publ. Univ. Pau, Pau, 2001,
MathSciNet.
Continuous Runge-Kutta-Nyström methods for initial value
problems with periodic solutions.
Papageorgiou, G.; Famelis, I. Th.
Numerical methods and computational mechanics (Miskolc, 1998).
Comput. Math. Appl. 42 (2001), no. 8-9, 1165--1176,
MathSciNet.
Application of Runge-Kutta-Merson algorithm for creep damage
analysis
Ling, Xiang; Tu, Shan-Tung; Gong, Jian-Ming
International Journal of Pressure Vessels and Piping, v 77, n 5,
Jun, 2000, p 243-248, Compendex.
On order 5 symplectic explicit Runge-Kutta Nyström
methods. McNabb Symposium, Part I (Auckland, 2000).
Chou, Lin-Yi; Sharp, P. W.
J. Appl. Math. Decis. Sci. 4 (2000), no. 2, 143--150,
MathSciNet.
A tenth order symplectic Runge-Kutta-Nyström method.
Tsitouras, Ch.
Celestial Mech. Dynam. Astronom. 74 (1999), no. 4, 223--230,
MathSciNet.
Gauss-Runge-Kutta-Nyström methods.
Burnton, Christopher; Scherer, Rudolf
BIT 38 (1998), no. 1, 12--21, MathSciNet.
A Runge-Kutta-Fehlberg procedure for numerical integration of
differential equations systems.
Dumitras, Daria Elena
Automat. Comput. Appl. Math. 6 (1997), no. 2, 42--45 (1998),
MathSciNet.
Higher-order explicit Runge-Kutta pairs with low stage
order
Verner, J.H.
Applied Numerical Mathematics, v 22, n 1-3, Nov, 1996, p 345-357,
Compendex.
Efficient Runge-Kutta (4,5) pair
Bogacki, P.; Shampine, L.F. Source:
Computers & Mathematics with Applications, v 32, n 6, Sep,
1996, p 15-28, Compendex.
Modified Runge-Kutta-Fehlberg methods for periodic
initial-value problems.
Simos, T. E.
Japan J. Indust. Appl. Math. 12 (1995), no. 1, 109--122,
MathSciNet.
Spreadsheet solution to an initial value problem using the
Runge-Kutta-Fehlberg method
Kharab, A.
Computer Applications in Engineering Education, v 2, n 2, 1994, p
129-134, Compendex.
A Runge-Kutta Fehlberg method with phase-lag of order infinity
for initial-value problems with oscillating solution.
Simos, T.E.
Computers & mathematics with applications, 1993, vol. 25, no.
6, pp. 95-101, Ingenta.
A Runge-Kutta-Fehlberg type procedure on two nodes for
numerical integration of systems differential
equations.
Dumitras, Daria Elena
Automat. Comput. Appl. Math. 2 (1993), no. 2, 139--143,
MathSciNet.
A low-order embedded Runge-Kutta method for periodic initial
value problems.
Sideridis, A. B.; Simos, T. E.
J. Comput. Appl.
Math. 44 (1992), no. 2, 235--244,
MathSciNet.
New continuous extensions for fifth-order RK formulas.
Calvo, M.; Montijano, J. I.; Rández, L.
Rev. Acad. Cienc. Zaragoza (2) 45 (1990), 69--81,
MathSciNet.
An Adaptive Boundary Value Runge-Kutta Solver for First Order
Boundary Value Problems
Suchitra Gupta
SIAM Journal on Numerical Analysis, Vol. 22, No. 1. (Feb., 1985),
pp. 114-126.
The Runge-Kutta-Fehlberg procedures for the numerical solution
of Volterra integral equations.
Micula, Maria
Studia Univ. Babeedla s-Bolyai Math. 26 (1981), no. 2, 56--61,
MathSciNet.
On the Runge-Kutta-Fehlberg method for the nonlinear itegral
equation of Volterra type. (Romanian)
Coroian, Iulian
Stud. Cerc. Mat. 26 (1974), 505--511, MathSciNet.
The approximate solution of a certain nonlinear Volterra type
integral equation by a bilateral method of Runge-Kutta-Fehlberg
form. (Russian)
Lomakovic, A. N.; Iscuk, V. A.
Vycisl. Prikl. Mat. (Kiev) No. 23 (1974), 29--40, 172--173,
MathSciNet.
Procedures of Runge-Kutta-Fehlberg type with error of order
,
for the approximation of solutions of first order
integrodifferential equations of Volterra type.
(Romanian)
Micula, Maria
Stud. Cerc. Mat. 25 (1973), 33--40, MathSciNet.
Procédés de type Runge-Kutta-Fehlberg pour
l'approximation de la solution de l'équation
intégrodifférential de premier ordre de type
Volterra. (French)
Micula, Maria
Studia Univ. Babes-Bolyai Ser. Math.-Mech. 18 (1973), no. 1,
61--68, MathSciNet.
Optimum Runge-Kutta-Fehlberg methods for second-order
differential equations.
Jain, R. K.; Jain, M. K.
J. Inst. Math. Appl. 10 (1972), 202--210,
MathSciNet.
Optimum Runge-Kutta Fehlberg methods for first order
differential equations.
Jain, R. K.; Jain, M. K.
J. Inst. Math. Appl. 8 (1971), 386--396,
MathSciNet.
Solution of integro-differential equations of Volterra type by
the Runge-Kutta-Fehlberg method. (Russian)
Lomakovic, A. N.
Vycisl. Prikl. Mat. (Kiev) No. 7 (1969), 64--76,
MathSciNet.
Zum Verfahren von Runge-Kutta-Fehlberg.
(German)
Filippi, Siegfried
Math.-Tech.-Wirtschaft 11 1964 147--153,
MathSciNet.
On the use of Runge-Kutta and Adams' methods in computer
practice. (Polish)
Dolhk abrowski, Mirosaw; Szoda, Zenon
Algorytmy Zeszyt Specjalny No. 1 1963 71--85,
MathSciNet.
Delimitation of the error in Fehlberg's procedure of numerical
integration of first order differential equations.
(Romanian)
Cotiu, A.
Studia Univ. Babes-Bolyai Ser. Math.-Phys. 7 1962 no. 2, 37--43,
MathSciNet.