1. 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.  
2. 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.  
3. Runge-Kutta-Nyström methods adapted to the numerical integration of perturbed oscillators.
   Franco, J. M.
   Comput. Phys. Comm. 147 (2002), no. 3, 770--787, MathSciNet.  
4. Algebraic conditions for high-order convergent deferred correction schemes based on Runge-Kutta-Nyström methods for second order boundary value problems.
   Van Daele, M.; Van Hecke, T.
   Ninth Seminar on Numerical Solution of Differential and Differential-Algebraic Equations (Halle, 2000). Appl. Numer. Math. 42 (2002), no. 1-3, 453--464, MathSciNet.  
5. Practical symplectic partitioned Runge-Kutta and Runge-Kutta-Nyström methods.
   Blanes, S.; Moan, P. C.
   J. Comput. Appl. Math. 142 (2002), no. 2, 313--330, MathSciNet.  
6. Fuzzy initial value problems based on the Runge-Kutta-Fehlberg method. (Chinese)  
   Wu, Qiang; Shen, Yu Bo
   Math. Theory Appl. (Changsha)  22  (2002),  no. 1, 72--74, MathSciNet.  
7. Mono-implicit Runge-Kutta-Nyström methods with application to boundary value ordinary differential equations.
   Muir, P. H.; Adams, M.
   BIT 41 (2001), no. 4, 776--799, MathSciNet.  
8. 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.  
9. High-order convergent deferred correction schemes based on parameterized Runge-Kutta-Nyström methods for second-order boundary value problems. Advanced numerical methods for mathematical modelling.
   Van Hecke, T.; Van Daele, M.
   J. Comput. Appl. Math. 132 (2001), no. 1, 107--125, MathSciNet.  
10. 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.  
11. 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.  
12. 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.  
13. 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.  
14. A tenth order symplectic Runge-Kutta-Nyström method.
    Tsitouras, Ch.
    Celestial Mech. Dynam. Astronom. 74 (1999), no. 4, 223--230, MathSciNet.  
15. High-order zero-dissipative Runge-Kutta-Nyström methods.
    Tsitouras, Ch.
    J. Comput. Appl. Math. 95 (1998), no. 1-2, 157--161, MathSciNet.  
16. Order bound for a family of parallel Runge-Kutta-Nyström methods through computer algebra.
    Paternoster, B.
    Comput. Math. Appl. 35 (1998), no. 9, 107--119, MathSciNet.  
17. Gauss-Runge-Kutta-Nyström methods.
    Burnton, Christopher; Scherer, Rudolf
    BIT 38 (1998), no. 1, 12--21, MathSciNet.  
18. Computation of the interval of stability of Runge-Kutta-Nyström methods.
    Paternoster, B.; Cafaro, M.
    J. Symbolic Comput. 25 (1998), no. 3, 383--394, MathSciNet.  
19. 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.  
20. On the generation of mono-implicit Runge-Kutta-Nyström methods by mono-implicit Runge-Kutta methods.
    De Meyer, H.; Vanden Berghe, G.; Van Hecke, T.; Van Daele, M.
    J. Comput. Appl. Math. 87 (1997), no. 1, 147--167, MathSciNet.  
21. The Runge-Kutta Theory in a Nutshell  
    Peter Albrecht
    SIAM Journal on Numerical Analysis, Vol. 33, No. 5. (Oct., 1996), pp. 1712-1735, Jstor.  
22. 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.
23. 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.
24. Explicit symmetric Runge-Kutta-Nyström methods for parallel computers.
    Cong, N. h.
    Comput. Math. Appl. 31 (1996), no. 2, 111--121, MathSciNet.  
25. 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.  
26. 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.
27. Canonical Runge-Kutta-Nyström methods of orders five and six.
    Okunbor, Daniel I.; Skeel, Robert D.
    J. Comput. Appl. Math. 51 (1994), no. 3, 375--382, MathSciNet.  
28. 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.  
29. 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.  
30. An improvement for parallel-iterated Runge-Kutta-Nyström methods.
    Nguyen Huu Cong
    Acta Math. Vietnam. 18 (1993), no. 2, 295--307, MathSciNet.  
31. High-order symplectic Runge-Kutta-Nyström methods.
    Calvo, M. P.; Sanz-Serna, J. M.
    SIAM J. Sci. Comput. 14 (1993), no. 5, 1237--1252, MathSciNet.  
32. A-stable diagonally implicit Runge-Kutta-Nyström methods for parallel computers.
    Nguyen Huu Cong
    Numer. Algorithms 4 (1993), no. 3, 263--281, MathSciNet.  
33. 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.  
34. An Explicit Runge-Kutta-Nystrom Method is Canonical If and Only If Its Adjoint is Explicit  
    Daniel Okunbor; Robert D. Skeel
    SIAM Journal on Numerical Analysis, Vol. 29, No. 2. (Apr., 1992), pp. 521-527, Jstor.  
35. Some Runge-Kutta formula pairs.  
    Verner, J. H.
    SIAM J. Numer. Anal.  28  (1991),  no. 2, 496--511, MathSciNet.  
36. A Contrast of Some Runge-Kutta Formula Pairs  
    J. H. Verner
    SIAM Journal on Numerical Analysis, Vol. 27, No. 5. (Oct., 1990), pp. 1332-1344, Jstor.  
37. 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.  
38. Two high-order multistep methods with offstep points applied with a variable stepsize.
    Filippi, S.; Schöne, F.
    J. Comput. Appl. Math. 30 (1990), no. 2, 155--164, MathSciNet.  
39. Runge-Kutta interpolants based on values from two successive integration steps.  
    Tsitouras, Ch.; Papageorgiou, G.
    Computing  43  (1990),  no. 3, 255--266, MathSciNet.  
40. Diagonally Implicit Runge-Kutta-Nystrom Methods for Oscillatory Problems  
    P. J. Van der Houwen; B. P. Sommeijer
    SIAM Journal on Numerical Analysis, Vol. 26, No. 2. (Apr., 1989), pp. 414-429, Jstor.  
41. Explicit Runge-Kutta (-Nystrom) Methods with Reduced Phase Errors for Computing Oscillating Solutions  
    P. J. Van der Houwen; B. P. Sommeijer
    SIAM Journal on Numerical Analysis, Vol. 24, No. 3. (Jun., 1987), pp. 595-617, Jstor.  
42. Some Practical Runge-Kutta Formulas  
    Lawrence F. Shampine
    Mathematics of Computation, Vol. 46, No. 173. (Jan., 1986), pp. 135-150, Jstor.  
43. 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.
44. Corrigenda: An Adaptive Boundary Value Runge-Kutta Solver for First Order Boundary Value Problems
    Suchitra Gupta
    SIAM Journal on Numerical Analysis, Vol. 22, No. 6. (Dec., 1985), p. 1255.
45. Bereiche der absoluten Stabilität zu den Runge-Kutta-Fehlberg-Formelpaaren für gewöhnliche Differentialgleichungen erster Ordnung. (German)
    [Regions of absolute stability for Runge-Kutta-Fehlberg pairs of formulas for ordinary differential equations of first order]    
    Fillippi, S.    
    Z. Angew. Math. Mech. 65 (1985), no. 7, 312--314, MathSciNet.  
46. An efficient Runge-Kutta-Fehlberg method.    
    Praagman, Niek    
    Delft Progr. Rep. 8 (1983), no. 2, 134--138, MathSciNet.  
47. Two Classes of Internally S-Stable Generalized Runge-Kutta Processes which Remain Consistent with an Inaccurate Jacobian  
    J. D. Day; D. N. P. Murthy
    Mathematics of Computation, Vol. 39, No. 160. (Oct., 1982), pp. 491-509, Jstor.  
48. 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.  
49. Explicit Runge-Kutta Methods with Estimates of the Local Truncation Error  
    J. H. Verner
    SIAM Journal on Numerical Analysis, Vol. 15, No. 4. (Aug., 1978), pp. 772-790, Jstor.  
50. Test Results on Initial Value Methods for Non-Stiff Ordinary Differential Equations  
    W. H. Enright; T. E. Hull  
    SIAM Journal on Numerical Analysis, Vol. 13, No. 6. (Dec., 1976), pp. 944-961, Jstor.  
51. A two-sided process of Runge-Kutta-Fehlberg type. (Russian)    
    Oleinik, A. G.    
    Approximate methods of mathematical analysis (Russian), pp. 71--79. Kiev. Gos. Ped. Inst., Kiev, 1976, MathSciNet.  
52. Solution of the direct geodesic problem on the surface of an ellipsoid by means of the Runge-Kutta-Englang method. (Russian)  
    Bespalov, N. A.; Saposnikov, A. I.
    Izv. Vyss. Ucebn. Zaved. Geod. i Aèrofot.  1976,  no. 3, 11--14, 133, MathSciNet.  
53. Two-sided methods of Runge-Kutta-Fehlberg type. (Russian)
    Ljascenko, N. Ja.; Oleinik, A. G.
    Vycisl. Prikl. Mat. (Kiev) Vyp. 29 (1976), 17--26, 151, MathSciNet.  
54. 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.  
55. 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.  
56. 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.  
57. 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.  
58. Procedures of Runge-Kutta-Fehlberg type, of order of exactness 5 and 6 on 2 and 3 nodes, for the numerical integration of systems of first order ordinary differential equations. (Romanian)    
    Cotiu, A.    
    Scientific Conference of the Teaching Staffs (1971), pp. 113--118. Cluj Politech. Inst., Cluj, 1973, MathSciNet.  
59. 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.  
60. 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.  
61. Procedures of Runge-Kutta-Fehlberg type, of order of exactness 5 and 6 on 2 and 3 nodes, for the numerical integration of systems of first order ordinary differential equations. (Romanian)
    Cotiu, A.
    Scientific Conference of the Teaching Staffs (1971), pp. 113--118. Cluj Politech. Inst., Cluj, 1973, MathSciNet.  
62. 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.  
63. Generalized Runge-Kutta Processes for Stable Systems with Large Lipschitz Constants  
    J. Douglas Lawson
    SIAM Journal on Numerical Analysis, Vol. 4, No. 3. (Sep., 1967), pp. 372-380, Jstor.  
64. Zum Verfahren von Runge-Kutta-Fehlberg. (German)    
    Filippi, Siegfried
    Math.-Tech.-Wirtschaft 11 1964 147--153, MathSciNet.  
65. 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.  
66. 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.  
67. Sur certaines extensions d'une transformation de Fehlberg. (Romanian)    
    Cotiu, A.    
    Bul. Sti. Inst. Politehn. Cluj 4 1961 45--54, MathSciNet.  

(c) John H. Mathews 2004