Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Comparing error estimators for Runge-Kutta methods

Authors: L. F. Shampine and H. A. Watts
Journal: Math. Comp. 25 (1971), 445-455
MSC: Primary 65L99
MathSciNet review: 0297138
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A way is proposed to compare local error estimators. This is applied to the major estimators for fourth-order Runge-Kutta procedures. An estimator which leads to a production code 18

References [Enhancements On Off] (What's this?)

  • [1] E. L. Ince, Ordinary Differential Equations, Dover Publications, New York, 1944. MR 0010757
  • [2] Jan Christiansen, Handbook Series Numerical Integration: Numerical solution of ordinary simultaneous differential equations of the 1st order using a method for automatic step change, Numer. Math. 14 (1970), no. 4, 317–324. MR 1553973,
  • [3] J. A. Zonneveld, Automatic numerical integration, Mathematical Centre Tracts, No. 8, Mathematisch Centrum, Amsterdam, 1964. MR 0171381
  • [4] T. E. Hull, The Numerical Integration of Ordinary Differential Equations, Proc. IFIP Congress 68, North-Holland, Amsterdam, 1968, pp. 131-144.
  • [5] Peter Henrici, Discrete variable methods in ordinary differential equations, John Wiley & Sons, Inc., New York-London, 1962. MR 0135729
  • [6] F. Ceschino and J. Kuntzmann, Numerical solution of initial value problems, Translated from the French by D. Boyanovitch, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1963. MR 0195262
  • [7] Henri Morel, Evaluation de l’erreur sur un pas dans la méthode de Runge-Kutta, C. R. Acad. Sci. Paris 243 (1956), 1999–2002 (French). MR 0082739
  • [8] R. England, Error estimates for Runge-Kutta type solutions to systems of ordinary differential equations, Comput. J. 12 (1969/1970), 166–170. MR 0242377,
  • [9] R. E. Jones, RUNKUT-Runge Kutta Integrator of Systems of First Order Ordinary Differential Equations, Report #SC-M-70-724, Sandia Laboratories, Albuquerque, New Mexico, 1970.
  • [10] L. F. Shampine & H. A. Watts, Efficient Runge-Kutta Codes, Report #SC-RR-70-615, Sandia Laboratories, Albuquerque, New Mexico, 1970. (This report is available from the authors or Sandia Laboratory, Division 3428.)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65L99

Retrieve articles in all journals with MSC: 65L99

Additional Information

Keywords: Local error, error estimators, Runge-Kutta methods, step size adjustment, solution of differential equations
Article copyright: © Copyright 1971 American Mathematical Society

American Mathematical Society