Bibliography for the Runge-Kutta Method

unabridged

  1. Accurate Numerical Simulation of Compressible Transitional Flows in Turbomachinery
    De Palma P.
    American Institute of Aeronautics and Astronautics Journal, 1 April 2002, vol. 40, no. 4, pp. 702-708(7), Ingenta.  
  2. Explicit Runge-Kutta pairs appropriate for engineering applications
    Tsitouras C.
    Applied Mathematical Modelling, January 2002, vol. 26, no. 1, pp. 77-88(12, Ingenta.  
  3. A modified phase-fitted Runge-Kutta method for the numerical solution of the Schrodinger equation
    Simos, T. E.; Aguiar, J. V.
    Journal of Mathematical Chemistry, 2001, vol. 30, no. 1, pp. 121-131, Ingenta.  
  4. Optimal implicit exponentially-fitted Runge-Kutta methods
    Vanden Berghe, G.; Ixaru, L. G.; Van Daele, M.
    Computer Physics Communications, 2001, vol. 140, no. ER3, pp. 346-357, Ingenta.  
  5. 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.  
  6. Analysis of non-linear singular system from fluid dynamics using extended Runge-Kutta methods.   
    Murugesan, K.; Dhayabaran, D. Paul; Evans, David J.    
    Int. J. Comput. Math. 76 (2000), no. 2, 239--266, MathSciNet.  
  7. A local-global version of a stepsize control for Runge-Kutta methods.    
    Kulikov, G. Yu.    
    Korean J. Comput. Appl. Math. 7 (2000), no. 2, 289--318, MathSciNet.  
  8. A new type of singly-implicit Runge-Kutta method. Auckland numerical ordinary differential equations (Auckland, 1998).    
    Butcher, J. C.; Chen, D. J. L.    
    Appl. Numer. Math. 34 (2000), no. 2-3, 179--188, MathSciNet.  
  9. On the numerical integration of orbital problems with high order Runge-Kutta-Nyström methods.    
    González, Ana B.; Martín, Pablo; López, David J.    
    Appl. Numer. Math. 35 (2000), no. 1, 1--10, MathSciNet.  
  10. Two-step Runge-Kutta: Theory and practice
    Tracogna, S.; Welfert, B. V.
    Bit, 2000, vol. 40, no. 4, pp. 775-799, Ingenta.  
  11. Explicit pseudo two-step Runge-Kutta methods for parallel computers.    
    Cong, Nguyen Huu    
    Int. J. Comput. Math. 73 (1999), no. 1, 77--91, MathSciNet.  
  12. Fifth-order Runge-Kutta with higher order derivative approximations.    
    Goeken, David; Johnson, Olin    
    Proceedings of the 15th Annual Conference of Applied Mathematics (Edmond, OK, 1999), 1--9 (electronic), Electron. J. Differ. Equ. Conf., 2, Southwest Texas State Univ., San Marcos, TX, 1999, MathSciNet.  
  13. Numerical Simulation of the Unsteady Flow Past a Hydrofoil.
    Landrini, Maurizio; Lugni, Claudio; Bertram, Volker
    Ship technology research, 1999, vol. 46, no. 1, pp. 14, Ingenta.  
  14. Runge-Kutta methods for linear ordinary differential equations.   
    Zingg, D. W.; Chisholm, T. T.    
    Appl. Numer. Math. 31 (1999), no. 2, 227--238, MathSciNet.  
  15. Runge-Kutta-Nyström-type parallel block predictor-corrector methods.    
    Cong, Nguyen Huu; Strehmel, Karl; Weiner, Rüdiger; Podhaisky, Helmut   
    Adv. Comput. Math. 10 (1999), no. 2, 115--133, MathSciNet.   
  16. A fourth order Runge-Kutta RK(4,4) method with error control.
    Yaakub, A. R.; Evans, D. J.
    Int. J. Comput. Math. 71 (1999), no. 3, 383--411, MathSciNet.  
  17. A new 3-stage fourth order Runge-Kutta composite method for solving initial value problems.
    Yaacob, N.; Evans, D. J.
    Int. J. Comput. Math. 72 (1999), no. 4, 541--546, MathSciNet.  
  18. On implicit schemes of Runge-Kutta type of the third order of approximation. (Russian)    
    Pinchukov, V. I.     
    Vychisl. Tekhnol. 4 (1999), no. 2, 59--73, MathSciNet.  
  19. An explicit Runge-Kutta method of order twenty-five. Solving differential equations on parallel computers.    
    Sommeijer, B. P.    
    CWI Quarterly 11 (1998), no. 1, 75--82, MathSciNet.  
  20. On the convergence of Runge-Kutta methods for stiff non-linear differential equations.    
    Calvo, M.; Gonzalez-Pinto, S.; Montijano, J. I.    
    Numer. Math. 81 (1998), no. 1, 31--51, MathSciNet.  
  21. The Runge-Kutta discontinuous Galerkin method for conservation laws. V. Multidimensional systems.    
    Cockburn, Bernardo; Shu, Chi-Wang    
    J. Comput. Phys. 141 (1998), no. 2, 199--224, MathSciNet.  
  22. Implicit-explicit Runge-Kutta methods for computing atmospheric reactive flows.
    Knoth, O.; Wolke, R.
    Applied numerical mathematics, 1998, vol. 28, no. 2/4, pp. 327, Ingenta.  
  23. Numerical procedures based on Runge-Kutta methods for solving isospectral flows.    
    Lopez, L.; Politi, T.    
    Appl. Numer. Math. 25 (1997), no. 4, 443--459, MathSciNet.  
  24. The Runge-Kutta Theory in a Nutshell  
    Peter Albrecht  
    SIAM Journal on Numerical Analysis, Vol. 33, No. 5. (Oct., 1996), pp. 1712-1735, Jstor.  
  25. A Global Convergence Theorem for a Class of Parallel Continuous Explicit Runge-Kutta Methods and Vanishing Lag Delay Differential Equations  
    Christopher T. H. Baker, Christopher A. H. Paul  
    SIAM Journal on Numerical Analysis, Vol. 33, No. 4. (Aug., 1996), pp. 1559-1576, Jstor.  
  26. 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.  
  27. A General Family of Explicit Runge-Kutta Pairs of Orders 6(5)  
    S. N. Papakostas, Ch. Tsitouras, G. Papageorgiou  
    SIAM Journal on Numerical Analysis, Vol. 33, No. 3. (Jun., 1996), pp. 917-936, Jstor.  
  28. A Note on Unconditional Maximum Norm Contractivity of Diagonally Split Runge-Kutta Methods  
    K. J. In'T Hout  
    SIAM Journal on Numerical Analysis, Vol. 33, No. 3. (Jun., 1996), pp. 1125-1134, Jstor.  
  29. Symplectic Partitioned Runge-Kutta Methods for Constrained Hamiltonian Systems  
    Laurent Jay  
    SIAM Journal on Numerical Analysis, Vol. 33, No. 1. (Feb., 1996), pp. 368-387, Jstor.  
  30. Explicit Runge-Kutta methods for initial value problems with oscillating solutions.    
    Calvo, M.; Franco, J. M.; Montijano, J. I.; Rández, L.    
    J. Comput. Appl. Math. 76 (1996), no. 1-2, 195--212, MathSciNet.  
  31. Implementation of two-step Runge-Kutta methods for ordinary differential equations.    
    Tracogna, S.    
    J. Comput. Appl. Math. 76 (1996), no. 1-2, 113--136, MathSciNet.  
  32. On error growth functions of Runge-Kutta methods. Special issue celebrating the centenary of Runge-Kutta methods.    
    Hairer, E.; Zennaro, M.    
    Appl. Numer. Math. 22 (1996), no. 1-3, 205--216, MathSciNet.  
  33. Highly stable parallel Runge-Kutta methods.    
    Bendtsen, Claus    
    Appl. Numer. Math. 21 (1996), no. 1, 1--8, MathSciNet.  
  34. Variable stepsize continuous two-step Runge-Kutta methods for ordinary differential equations.    
    Jackiewicz, Z.; Tracogna, S.    
    Numer. Algorithms 12 (1996), no. 3-4, 347--368, MathSciNet.  
  35. Runge-Kutta methods: some historical notes.
    Butcher, J. C.; Wanner, G.
    Special issue celebrating the centenary of Runge-Kutta methods. Appl. Numer. Math. 22 (1996), no. 1-3, 113--151, MathSciNet.  
  36. A history of Runge-Kutta methods.
    Butcher, J.C.
    Applied numerical mathematics, 1996, vol. 20, no. 3, pp. 247, Ingenta.  
  37. A New Recurrence for Computing Runge-Kutta Truncation Error Coefficients  
    M. E. Hosea  
    SIAM Journal on Numerical Analysis, Vol. 32, No. 6. (Dec., 1995), pp. 1989-2001, Jstor.  
  38. 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.  
  39. Runge-Kutta Solutions of Stiff Differential Equations Near Stationary Points  
    Ch. Lubich, K. Nipp, D. Stoffer  
    SIAM Journal on Numerical Analysis, Vol. 32, No. 4. (Aug., 1995), pp. 1296-1307, Jstor.  
  40. 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.   
  41. Runge-Kutta Approximation of Quasi-Linear Parabolic Equations  
    Christian Lubich, Alexander Ostermann  
    Mathematics of Computation, Vol. 64, No. 210. (Apr., 1995), pp. 601-627, Jstor.  
  42. The Potential for Parallelism in Runge-Kutta Methods. Part 1: RK Formulas in Standard Form  
    K. R. Jackson, S. P. Norsett
    SIAM Journal on Numerical Analysis, Vol. 32, No. 1. (Feb., 1995), pp. 49-82, Jstor.  
  43. A New Fourth Order Runge-Kutta Formula Based on the Contra-Harmonic (CoM) Mean.
    Evans, D.J.; Yaakub, A.R.
    International journal of computer mathematics, 1995, vol. 57, no. 3/4, pp. 249, Ingenta.  
  44. Runge-Kutta Methods for Dissipative and Gradient Dynamical Systems  
    A. R. Humphries, A. M. Stuart  
    SIAM Journal on Numerical Analysis, Vol. 31, No. 5. (Oct., 1994), pp. 1452-1485, Jstor.  
  45. Completely Imbedded Runge-Kutta Pairs  
    P. W. Sharp, J. H. Verner  
    SIAM Journal on Numerical Analysis, Vol. 31, No. 4. (Aug., 1994), pp. 1169-1190, Jstor.  
  46. Stability of Runge-Kutta Methods for Stiff Ordinary Differential Equations  
    Roger K. Alexander  
    SIAM Journal on Numerical Analysis, Vol. 31, No. 4. (Aug., 1994), pp. 1147-1168, Jstor.  
  47. Order Results for Mono-Implicit Runge-Kutta Methods  
    K. Burrage, F. H. Chipman, P. H. Muir  
    SIAM Journal on Numerical Analysis, Vol. 31, No. 3. (Jun., 1994), pp. 876-891, Jstor.  
  48. B-Convergence Properties of Multistep Runge-Kutta Methods  
    Shoufu Li  
    Mathematics of Computation, Vol. 62, No. 206. (Apr., 1994), pp. 565-575, Jstor.  
  49. Complete Algebraic Characterization of A-Stable Runge-Kutta Methods  
    R. Scherer, W. Wendler  
    SIAM Journal on Numerical Analysis, Vol. 31, No. 2. (Apr., 1994), pp. 540-551, Jstor.  
  50. Contractivity of Waveform Relaxation Runge-Kutta Iterations and Related Limit Methods for Dissipative Systems in the Maximum Norm  
    A. Bellen, Z. Jackiewicz, M. Zennaro  
    SIAM Journal on Numerical Analysis, Vol. 31, No. 2. (Apr., 1994), pp. 499-523, Jstor.  
  51. B-Convergence Properties of Multistep Runge-Kutta Methods  
    Shoufu Li  
    Mathematics of Computation, Vol. 62, No. 206. (Apr., 1994), pp. 565-575, Jstor.  
  52. Application of the fourth-order Runge-Kutta method for the solution of high-order general initial value problems.
    Cortell, R.
    Comput. & Structures 49 (1993), no. 5, 897--900 (1994), MathSciNet.  
  53. Estimating the Error of the Classic Runge-Kutta Formula
    Hosea, M. E.; Shampine, L. F.
    Applied mathematics and computation, 1994, vol. 66, no. 2/3, pp. 217, Ingenta.  
  54. A New Fourth Order Runge-Kutta Formula Based on the Harmonic Mean.
    Sanugi, B. B.; Evans, D. J.
    International journal of computer mathematics, 1994, vol. 50, no. 1/2, pp. 113, Ingenta.  
  55. Differentiable Interpolants for High-Order Runge-Kutta Methods  
    J. H. Verner  
    SIAM Journal on Numerical Analysis, Vol. 30, No. 5. (Oct., 1993), pp. 1446-1466, Jstor.  
  56. Order Barriers and Characterizations for Continuous Mono-Implicit Runge- Kutta Schemes  
    Paul Muir, Brynjulf Owren  
    Mathematics of Computation, Vol. 61, No. 204. (Oct., 1993), pp. 675-699, Jstor.  
  57. 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.  
  58. Half-Explicit Runge-Kutta Methods for Differential-Algebraic Systems of Index 2  
    V. Brasey, E. Hairer  
    SIAM Journal on Numerical Analysis, Vol. 30, No. 2. (Apr., 1993), pp. 538-552, Jstor.  
  59. Partitioned Runge-Kutta Methods for Separable Hamiltonian Problems  
    L. Abia, J. M. Sanz-Serna  
    Mathematics of Computation, Vol. 60, No. 202. (Apr., 1993), pp. 617-634, Jstor.  
  60. 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.  
  61. Runge-Kutta Methods for Parabolic Equations and Convolution Quadrature  
    Ch. Lubich, A. Ostermann  
    Mathematics of Computation, Vol. 60, No. 201. (Jan., 1993), pp. 105-131, Jstor.  
  62. Runge-Kutta Methods for Partial Differential Equations and Fractional Orders of Convergence  
    A. Ostermann, M. Roche  
    Mathematics of Computation, Vol. 59, No. 200. (Oct., 1992), pp. 403-420, Jstor.  
  63. 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.  
  64. 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.  
  65. An Optimal Runge-Kutta Method for Steady-State Solutions of Hyperbolic Systems  
    Chichia Chiu, David A. Kopriva  
    SIAM Journal on Numerical Analysis, Vol. 29, No. 2. (Apr., 1992), pp. 425-438, Jstor.  
  66. Embedded Diagonally Implicit Runge-Kutta Algorithms on Parallel Computers  
    P. J. Van Der Houwen, B. P. Sommeijer, W. Couzy  
    Mathematics of Computation, Vol. 58, No. 197. (Jan., 1992), pp. 135-159, Jstor.  
  67. Embedded Pseudo-Runge-Kutta Methods  
    Masaharu Nakashima  
    SIAM Journal on Numerical Analysis, Vol. 28, No. 6. (Dec., 1991), pp. 1790-1802, Jstor.  
  68. 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.  
  69. Order Conditions for Canonical Runge-Kutta Schemes  
    J. M. Sanz-Serna, L. Abia  
    SIAM Journal on Numerical Analysis, Vol. 28, No. 4. (Aug., 1991), pp. 1081-1096, Jstor.  
  70. Projected Implicit Runge-Kutta Methods for Differential-Algebraic Equations  
    Uri M. Ascher, Linda R. Petzold  
    SIAM Journal on Numerical Analysis, Vol. 28, No. 4. (Aug., 1991), pp. 1097-1120, Jstor.  
  71. 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.  
  72. Asymptotically Efficient Runge-Kutta Methods for a Class of Ito and Stratonovich Equations  
    Nigel J. Newton  
    SIAM Journal on Applied Mathematics, Vol. 51, No. 2. (Apr., 1991), pp. 542-567, Jstor.  
  73. Order Barriers for Continuous Explicit Runge-Kutta Methods  
    Brynjulf Owren, Marino Zennaro  
    Mathematics of Computation, Vol. 56, No. 194. (Apr., 1991), pp. 645-661, Jstor.  
  74. Some Runge-Kutta Formula Pairs  
    J. H. Verner  
    SIAM Journal on Numerical Analysis, Vol. 28, No. 2. (Apr., 1991), pp. 496-511, Jstor.  
  75. 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.   
  76. Two-Step Runge-Kutta Methods and Hyperbolic Partial Differential Equations  
    R. A. Renaut  
    Mathematics of Computation, Vol. 55, No. 192. (Oct., 1990), pp. 563-579, Jstor.  
  77. Runge-Kutta Methods and Differential-Algebraic Systems  
    Roger K. Alexander, James J. Coyle  
    SIAM Journal on Numerical Analysis, Vol. 27, No. 3. (Jun., 1990), pp. 736-752, Jstor.  
  78. Towards Efficient Runge-Kutta Methods for Stiff Systems  
    J. C. Butcher, J. R. Cash  
    SIAM Journal on Numerical Analysis, Vol. 27, No. 3. (Jun., 1990), pp. 753-761.
  79. Galerkin/Runge-Kutta Discretizations for Semilinear Parabolic Equations  
    Stephen L. Keeling  
    SIAM Journal on Numerical Analysis, Vol. 27, No. 2. (Apr., 1990), pp. 394-418.
  80. On Order Reduction for Runge-Kutta Methods Applied to Differential/ Algebraic Systems and to Stiff Systems of Odes  
    Kevin Burrage, Linda Petzold  
    SIAM Journal on Numerical Analysis, Vol. 27, No. 2. (Apr., 1990), pp. 447-456, Jstor.  
  81. Runge-Kutta Methods Applied to Fully Implicit Differential-Algebraic Equations of Index 1  
    Anne Kvaerno  
    Mathematics of Computation, Vol. 54, No. 190. (Apr., 1990), pp. 583-625, Jstor.  
  82. The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case  
    Bernardo Cockburn, Suchung Hou, Chi-Wang Shu  
    Mathematics of Computation, Vol. 54, No. 190. (Apr., 1990), pp. 545-581.
  83. The Numerical Analysis of Implicit Runge-Kutta Methods for a Certain Nonlinear Integro-Differential Equation  
    Yuan Wei, Tang Tao  
    Mathematics of Computation, Vol. 54, No. 189. (Jan., 1990), pp. 155-168, Jstor.  
  84. Implicit Runge-Kutta Methods for Differential Algebraic Equations  
    Michel Roche  
    SIAM Journal on Numerical Analysis, Vol. 26, No. 4. (Aug., 1989), pp. 963-975, Jstor.  
  85. Analysis of Error Control Strategies for Continuous Runge-Kutta Methods  
    W. H. Enright  
    SIAM Journal on Numerical Analysis, Vol. 26, No. 3. (Jun., 1989), pp. 588-599.
  86. 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.  
  87. Phase-Lag Analysis of Implicit Runge-Kutta Methods  
    P. J. Van der Houwen, B. P. Sommeijer  
    SIAM Journal on Numerical Analysis, Vol. 26, No. 1. (Feb., 1989), pp. 214-229, Jstor.  
  88. Natural Continuous Extensions of Runge-Kutta Methods for Volterra Integral Equations of the Second Kind and Their Applications
    A. Bellen, Z. Jackiewicz, R. Vermiglio, M. Zennaro  
    Mathematics of Computation, Vol. 52, No. 185. (Jan., 1989), pp. 49-63, Jstor.  
  89. A Block 6(4) Runge-Kutta Formula for Nonstiff Initial Value Problems.
    Cash, J.R.
    Acm transactions on mathematical software, 1989, vol. 15, no. 1, pp. 15, Ingenta.  
  90. Stability Properties of Interpolants for Runge-Kutta Methods  
    Alfredo Bellen, Marino Zennaro  
    SIAM Journal on Numerical Analysis, Vol. 25, No. 2. (Apr., 1988), pp. 411-432, Jstor.  
  91. High Order Algebraically Stable Multistep Runge-Kutta Methods  
    K. Burrage  
    SIAM Journal on Numerical Analysis, Vol. 24, No. 1. (Feb., 1987), pp. 106-115.
  92. 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.  
  93. On the Algebraic Equations in Implicit Runge-Kutta Methods  
    W. H. Hundsdorfer, M. N. Spijker  
    SIAM Journal on Numerical Analysis, Vol. 24, No. 3. (Jun., 1987), pp. 583-594, Jstor.  
  94. Some remarks on the intervals of stability of Runge Kutta methods after Richardson extrapolation.   
    Olejniczak, A.   
    Zastos. Mat. 19 (1987), no. 2, 335--339, MathSciNet.  
  95. Some Practical Runge-Kutta Formulas  
    Lawrence F. Shampine  
    Mathematics of Computation, Vol. 46, No. 173. (Jan., 1986), pp. 135-150, Jstor.   
  96. Natural Continuous Extensions of Runge-Kutta Methods  
    M. Zennaro  
    Mathematics of Computation, Vol. 46, No. 173. (Jan., 1986), pp. 119-133, Jstor.   
  97. Order Results for Implicit Runge-Kutta Methods Applied to Differential/ Algebraic Systems  
    L. R. Petzold  
    SIAM Journal on Numerical Analysis, Vol. 23, No. 4. (Aug., 1986), pp. 837-852, Jstor.   
  98. On Runge-Kutta Methods for Parabolic Problems with Time-Dependent Coefficients  
    Ohannes A. Karakashian  
    Mathematics of Computation, Vol. 47, No. 175. (Jul., 1986), pp. 77-101, Jstor.   
  99. Modification of a one-step rational method of Runge-Kutta type of the fourth order. (Russian)
    Didukh, I. I.
    Vestnik L'vov. Politekhn. Inst. No. 202 (1986), 36--38, 148, MathSciNet.  
  100. Interpolation for Runge-Kutta Methods  
    Lawrence F. Shampine  
    SIAM Journal on Numerical Analysis, Vol. 22, No. 5. (Oct., 1985), pp. 1014-1027, Jstor.  
  101. 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.  
  102. Order Results for Implicit Runge-Kutta Methods Applied to Stiff Systems  
    Reinhard Frank, Josef Schneid, Christoph W. Ueberhuber  
    SIAM Journal on Numerical Analysis, Vol. 22, No. 3. (Jun., 1985), pp. 515-534, Jstor.  
  103. 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.  
  104. Implicit Runge-Kutta Methods of Optimal Order for Volterra Integro-Differential Equations  
    Hermann Brunner  
    Mathematics of Computation, Vol. 42, No. 165. (Jan., 1984), pp. 95-109, Jstor.  
  105. Additive Runge-Kutta Methods for Stiff Ordinary Differential Equations  
    G. J. Cooper, A. Sayfy  
    Mathematics of Computation, Vol. 40, No. 161. (Jan., 1983), pp. 207-218, Jstor.  
  106. Block Runge-Kutta Methods for the Numerical Integration of Initial Value Problems in Ordinary Differential Equations Part I. The Nonstiff Case  
    J. R. Cash  
    Mathematics of Computation, Vol. 40, No. 161. (Jan., 1983), pp. 175-191, Jstor.  
  107. Block Runge-Kutta Methods for the Numerical Integration of Initial Value Problems in Ordinary Differential Equations Part I. The Nonstiff Case  
    J. R. Cash  
    Mathematics of Computation, Vol. 40, No. 161. (Jan., 1983), pp. 175-191, Jstor.  
  108. Complete solutions of equations of conditions for four-stage fourth order Runge-Kutta-Nyström method.
    Sharma, S. R.
    Indian J. Pure Appl. Math. 14 (1983), no. 6, 692--698, MathSciNet.  
  109. Efficiently Implementable Algebraically Stable Runge-Kutta Methods  
    Kevin Burrage  
    SIAM Journal on Numerical Analysis, Vol. 19, No. 2. (Apr., 1982), pp. 245-258., Jstor.  
  110. 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.  
  111. On a common feature of some Runge-Kutta and predictor-corrector methods.   
    Marzulli, P.   
    Calcolo 16 (1979), no. 2, 181--188, MathSciNet.   
  112. 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.  
  113. On the BN Stability of the Runge-Kutta Methods  
    Giuseppe Piazza  
    Mathematics of Computation, Vol. 37, No. 156. (Oct., 1981), pp. 399-401, Jstor.  
  114. Stability Criteria for Implicit Runge-Kutta Methods  
    Kevin Burrage, J. C. Butcher  
    SIAM Journal on Numerical Analysis, Vol. 16, No. 1. (Feb., 1979), pp. 46-57, Jstor.  
  115. Families of Imbedded Runge-Kutta Methods  
    J. H. Verner  
    SIAM Journal on Numerical Analysis, Vol. 16, No. 5. (Oct., 1979), pp. 857-875, Jstor.  
  116. Stabilized Runge-Kutta Methods for Second Order Differential Equations without First Derivatives  
    P. J. Van der Houwen  
    SIAM Journal on Numerical Analysis, Vol. 16, No. 3. (Jun., 1979), pp. 523-537, Jstor.  
  117. Semiexplicit A-Stable Runge-Kutta Methods  
    G. J. Cooper, A. Sayfy  
    Mathematics of Computation, Vol. 33, No. 146. (Apr., 1979), pp. 541-556, Jstor.  
  118. 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.  
  119. 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.  
  120. 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.  
  121. An Efficient Solution Process for Implicit Runge-Kutta Methods  
    Theodore A. Bickart  
    SIAM Journal on Numerical Analysis, Vol. 14, No. 6. (Dec., 1977), pp. 1022-1027, Jstor.  
  122. Diagonally Implicit Runge-Kutta Methods for Stiff O.D.E.'s  
    Roger Alexander  
    SIAM Journal on Numerical Analysis, Vol. 14, No. 6. (Dec., 1977), pp. 1006-1021, Jstor.  
  123. A Curiosity of Low-Order Explicit Runge-Kutta Methods  
    J. Oliver  
    Mathematics of Computation, Vol. 29, No. 132. (Oct., 1975), pp. 1032-1036, Jstor.  
  124. 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.  
  125. Actual Order of Convergence of Runge-Kutta Methods on Differential Equations with Discontinuities  
    Bruce A. Chartres, Robert S. Stepleman  
    SIAM Journal on Numerical Analysis, Vol. 11, No. 6. (Dec., 1974), pp. 1193-1206, Jstor.  
  126. Contribution to the numerical solution of differential equations by means of Runge-Kutta formulas with Newton-Cotes numbers weights.
    Hut'a, Anton
    Acta Fac. Rerum Natur. Univ. Comenian. Math. Publ. 28 (1972), 51--65, MathSciNet.  
  127. 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.  
  128. 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.  
  129. Step size adjustment at discontinuities for fourth order Runge-Kutta methods.
    O'Regan, P. G.
    Comput. J. 13 1970 401--404, MathSciNet.  
  130. On the optimal choice of fourth-order Runge-Kutta formulas.
    Luther, H. A.; Sierra, H. G.
    Numer. Math. 15 1970 354--358, MathSciNet.  
  131. 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.  
  132. An Explicit Sixth-Order Runge-Kutta Formula (in Technical Notes and Short Papers)  
    H. A. Luther  
    Mathematics of Computation, Vol. 22, No. 102. (Apr., 1968), pp. 434-436, Jstor.  
  133. An Order Six Runge-Kutta Process with Extended Region of Stability  
    J. Douglas Lawson  
    SIAM Journal on Numerical Analysis, Vol. 4, No. 4. (Dec., 1967), pp. 620-625, Jstor.  
  134. A Runge-Kutta for all Seasons  
    J. Barkley Rosser  
    SIAM Review, Vol. 9, No. 3. (Jul., 1967), pp. 417-452, Jstor.  
  135. 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.  
  136. Further Explicit Fifth-Order Runge-Kutta Formulas  
    H. A. Luther  
    SIAM Review, Vol. 8, No. 3. (Jul., 1966), pp. 374-380, Jstor.  
  137. Runge-Kutta Methods with Constrained Minimum Error Bounds  
    Richard King  
    Mathematics of Computation, Vol. 20, No. 95. (Jul., 1966), pp. 386-391, Jstor.  
  138. Economical Evaluation of Runge-Kutta Formulae  
    David J. Fyfe  
    Mathematics of Computation, Vol. 20, No. 95. (Jul., 1966), pp. 392-398, Jstor.  
  139. Stability of the fourth order Runge-Kutta method for the solution of systems of differential equations.
    Abdel Karim, Abbas I.
    Comput. J. 9 1966 308--311, MathSciNet.  
  140. Some Fifth-Order Classical Runge-Kutta Formulas  
    H. A. Luther, H. P. Konen  
    SIAM Review, Vol. 7, No. 4. (Oct., 1965), pp. 551-558.
  141. 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.  
  142. On the Attainable Order of Runge-Kutta Methods  
    J. C. Butcher  
    Mathematics of Computation, Vol. 19, No. 91. (Jul., 1965), pp. 408-417, Jstor.  
  143. Implicit Runge-Kutta Processes
    J. C. Butcher
    Mathematics of Computation, Vol. 18, No. 85. (Jan., 1964), pp. 50-64.
  144. Optimum Runge-Kutta Methods (in Technical Notes and Short Papers)  
    T. E. Hull, R. L. Johnston  
    Mathematics of Computation, Vol. 18, No. 86. (Apr., 1964), pp. 306-310, Jstor.  
  145. Runge-Kutta Methods with Minimum Error Bounds  
    Anthony Ralston  
    Mathematics of Computation, Vol. 16, No. 80. (Oct., 1962), pp. 431-437, Jstor.  
  146. A Modification of the Runge-Kutta Fourth-Order Method  
    E. K. Blum  
    Mathematics of Computation, Vol. 16, No. 78. (Apr., 1962), pp. 176-187.
  147. 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.
  148. Note on the Runge-Kutta method.
    Milne, W. E.
    J. Research Nat. Bur. Standards 44, (1950). 549--550, MathSciNet.  

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003