Bibliography for the Runge-Kutta Method

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  1. Explicit Runge-Kutta pairs appropriate for engineering applications
    Tsitouras C.
    Applied Mathematical Modelling, January 2002, vol. 26, no. 1, pp. 77-88(12, Ingenta.  
  2. 100 Years of the Runge-Kutta method: a brief editing for schools  
    Bockmann, C.; Bruckner, A.  
    Teaching Mathematics and Its Applications, 2001, vol. 20, no. 1, pp. 25-49, Ingenta.  
  3. Runge-Kutta methods for linear ordinary differential equations.   
    Zingg, D. W.; Chisholm, T. T.    
    Appl. Numer. Math. 31 (1999), no. 2, 227--238, MathSciNet.  
  4. The Runge-Kutta Theory in a Nutshell  
    Peter Albrecht  
    SIAM Journal on Numerical Analysis, Vol. 33, No. 5. (Oct., 1996), pp. 1712-1735, Jstor.  
  5. A Family of Fifth-Order Runge-Kutta Pairs  
    S. N. Papakostas, G. Papageorgiou  
    Mathematics of Computation, Vol. 65, No. 215. (Jul., 1996), pp. 1165-1181, Jstor.  
  6. A General Class of Two-Step Runge-Kutta Methods for Ordinary Differential Equations  
    Z. Jackiewicz, S. Tracogna  
    SIAM Journal on Numerical Analysis, Vol. 32, No. 5. (Oct., 1995), pp. 1390-1427, Jstor.  
  7. Continuous Explicit Runge-Kutta Methods of Order 5  
    J. H. Verner, M. Zennaro  
    Mathematics of Computation, Vol. 64, No. 211. (Jul., 1995), pp. 1123-1146, Jstor.   
  8. The Relative Efficiency of Alternative Defect Control Schemes for High- Order Continuous Runge-Kutta Formulas  
    W. H. Enright  
    SIAM Journal on Numerical Analysis, Vol. 30, No. 5. (Oct., 1993), pp. 1419-1445, Jstor.  
  9. Runge-Kutta Methods and Local Uniform Grid Refinement  
    R. A. Trompert, J. G. Verwer  
    Mathematics of Computation, Vol. 60, No. 202. (Apr., 1993), pp. 591-616, Jstor.  
  10. Variable-Stepsize Explicit Two-Step Runge-Kutta Methods  
    Z. Jackiewicz, M. Zennaro  
    Mathematics of Computation, Vol. 59, No. 200. (Oct., 1992), pp. 421-438, Jstor.  
  11. 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.  
  12. On the Implementation of Singly Implicit Runge-Kutta Methods  
    G. J. Cooper  
    Mathematics of Computation, Vol. 57, No. 196. (Oct., 1991), pp. 663-672, Jstor.  
  13. Two-Step Runge-Kutta Methods  
    Z. Jackiewicz, R. Renaut, A. Feldstein  
    SIAM Journal on Numerical Analysis, Vol. 28, No. 4. (Aug., 1991), pp. 1165-1182, Jstor.  
  14. Some Runge-Kutta Formula Pairs  
    J. H. Verner  
    SIAM Journal on Numerical Analysis, Vol. 28, No. 2. (Apr., 1991), pp. 496-511, Jstor.  
  15. 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.   
  16. High Order Algebraically Stable Multistep Runge-Kutta Methods  
    K. Burrage  
    SIAM Journal on Numerical Analysis, Vol. 24, No. 1. (Feb., 1987), pp. 106-115.
  17. A New Theoretical Approach to Runge-Kutta Methods  
    Peter Albrecht  
    SIAM Journal on Numerical Analysis, Vol. 24, No. 2. (Apr., 1987), pp. 391-406, Jstor.  
  18. Some Practical Runge-Kutta Formulas  
    Lawrence F. Shampine  
    Mathematics of Computation, Vol. 46, No. 173. (Jan., 1986), pp. 135-150, Jstor.   
  19. Natural Continuous Extensions of Runge-Kutta Methods  
    M. Zennaro  
    Mathematics of Computation, Vol. 46, No. 173. (Jan., 1986), pp. 119-133, Jstor.   
  20. Interpolation for Runge-Kutta Methods  
    Lawrence F. Shampine  
    SIAM Journal on Numerical Analysis, Vol. 22, No. 5. (Oct., 1985), pp. 1014-1027, Jstor.  
  21. Stability Properties of Implicit Runge-Kutta Methods  
    Reinhard Frank, Josef Schneid, Christoph W. Ueberhuber  
    SIAM Journal on Numerical Analysis, Vol. 22, No. 3. (Jun., 1985), pp. 497-514, Jstor.  
  22. On the Stability of Volterra-Runge-Kutta Methods  
    E. Hairer, Ch. Lubich  
    SIAM Journal on Numerical Analysis, Vol. 21, No. 1. (Feb., 1984), pp. 123-135, Jstor.  
  23. Efficiently Implementable Algebraically Stable Runge-Kutta Methods  
    Kevin Burrage  
    SIAM Journal on Numerical Analysis, Vol. 19, No. 2. (Apr., 1982), pp. 245-258., Jstor.  
  24. Algebraically Stable and Implementable Runge-Kutta Methods of High Order  
    E. Hairer, G. Wanner  
    SIAM Journal on Numerical Analysis, Vol. 18, No. 6. (Dec., 1981), pp. 1098-1108, Jstor.  
  25. On the Efficient Implementation of Implicit Runge-Kutta Methods  
    J. M. Varah  
    Mathematics of Computation, Vol. 33, No. 146. (Apr., 1979), pp. 557-561, Jstor.  
  26. A Theoretical Criterion for Comparing Runge-Kutta Formulas  
    K. R. Jackson, W. H. Enright, T. E. Hull  
    SIAM Journal on Numerical Analysis, Vol. 15, No. 3. (Jun., 1978), pp. 618-641, Jstor.  
  27. A Curiosity of Low-Order Explicit Runge-Kutta Methods  
    J. Oliver  
    Mathematics of Computation, Vol. 29, No. 132. (Oct., 1975), pp. 1032-1036, Jstor.  
  28. An Order Bound for Runge-Kutta Methods  
    J. C. Butcher  
    SIAM Journal on Numerical Analysis, Vol. 12, No. 3. (Jun., 1975), pp. 304-315, Jstor.  
  29. Some Explicit Runge-Kutta Methods of High Order  
    G. J. Cooper, J. H. Verner  
    SIAM Journal on Numerical Analysis, Vol. 9, No. 3. (Sep., 1972), pp. 389-405, Jstor.  
  30. Comparing Error Estimators for Runge-Kutta Methods  
    L. F. Shampine, H. A. Watts  
    Mathematics of Computation, Vol. 25, No. 115. (Jul., 1971), pp. 445-455, Jstor.  
  31. The Complete Solution of the Fifth Order Runge-Kutta Equations  
    C. R. Cassity  
    SIAM Journal on Numerical Analysis, Vol. 6, No. 3. (Sep., 1969), pp. 432-436, Jstor.  
  32. A Runge-Kutta for all Seasons  
    J. Barkley Rosser  
    SIAM Review, Vol. 9, No. 3. (Jul., 1967), pp. 417-452, Jstor.  
  33. Solutions of the Fifth-Order Runge-Kutta Equations  
    C. R. Cassity  
    SIAM Journal on Numerical Analysis, Vol. 3, No. 4. (Dec., 1966), pp. 598-606, Jstor.  
  34. Further Explicit Fifth-Order Runge-Kutta Formulas  
    H. A. Luther  
    SIAM Review, Vol. 8, No. 3. (Jul., 1966), pp. 374-380, Jstor.  
  35. Economical Evaluation of Runge-Kutta Formulae  
    David J. Fyfe  
    Mathematics of Computation, Vol. 20, No. 95. (Jul., 1966), pp. 392-398, Jstor.  
  36. Some Fifth-Order Classical Runge-Kutta Formulas  
    H. A. Luther, H. P. Konen  
    SIAM Review, Vol. 7, No. 4. (Oct., 1965), pp. 551-558.
  37. An Order Five Runge-Kutta Process with Extended Region of Stability  
    J. Douglas Lawson  
    SIAM Journal on Numerical Analysis, Vol. 3, No. 4. (Dec., 1966), pp. 593-597, Jstor.  
  38. On the Attainable Order of Runge-Kutta Methods  
    J. C. Butcher  
    Mathematics of Computation, Vol. 19, No. 91. (Jul., 1965), pp. 408-417, Jstor.  
  39. A Modification of the Runge-Kutta Fourth-Order Method  
    E. K. Blum  
    Mathematics of Computation, Vol. 16, No. 78. (Apr., 1962), pp. 176-187.
  40. On the Accuracy of Runge-Kutta's Method  
    Max Lotkin  
    Mathematical Tables and Other Aids to Computation, Vol. 5, No. 35. (Jul., 1951), pp. 128-133.

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003