Bibliography for the Runge-Kutta-Fehlberg Method

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  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. 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.  
  4. 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.  
  5. 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.  
  6. 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.  
  7. 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.  
  8. A tenth order symplectic Runge-Kutta-Nyström method.
    Tsitouras, Ch.
    Celestial Mech. Dynam. Astronom. 74 (1999), no. 4, 223--230, MathSciNet.  
  9. Gauss-Runge-Kutta-Nyström methods.
    Burnton, Christopher; Scherer, Rudolf
    BIT 38 (1998), no. 1, 12--21, MathSciNet.  
  10. 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.  
  11. The Runge-Kutta Theory in a Nutshell  
    Peter Albrecht
    SIAM Journal on Numerical Analysis, Vol. 33, No. 5. (Oct., 1996), pp. 1712-1735, Jstor.  
  12. 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.
  13. 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.
  14. 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.  
  15. 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.
  16. 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.  
  17. 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.  
  18. 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.  
  19. 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.  
  20. Some Runge-Kutta formula pairs.  
    Verner, J. H.
    SIAM J. Numer. Anal.  28  (1991),  no. 2, 496--511, MathSciNet.  
  21. 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.  
  22. 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.  
  23. 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.  
  24. 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.  
  25. Some Practical Runge-Kutta Formulas  
    Lawrence F. Shampine
    Mathematics of Computation, Vol. 46, No. 173. (Jan., 1986), pp. 135-150, Jstor.  
  26. 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.
  27. An efficient Runge-Kutta-Fehlberg method.    
    Praagman, Niek    
    Delft Progr. Rep. 8 (1983), no. 2, 134--138, MathSciNet.  
  28. 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.  
  29. 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.  
  30. 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.  
  31. 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.  
  32. 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.  
  33. 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.  
  34. Procedures of Runge-Kutta-Fehlberg type with error of order [Graphics:../Images/RungeKuttaFehlbergBib_gr_1.gif], for the approximation of solutions of first order integrodifferential equations of Volterra type. (Romanian)    
    Micula, Maria    
    Stud. Cerc. Mat. 25 (1973), 33--40, MathSciNet.  
  35. 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.  
  36. 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.  
  37. 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.  
  38. 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.  
  39. 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.  
  40. Zum Verfahren von Runge-Kutta-Fehlberg. (German)    
    Filippi, Siegfried
    Math.-Tech.-Wirtschaft 11 1964 147--153, MathSciNet.  
  41. 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.  
  42. 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.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004