Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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



Efficient Runge-Kutta integrators for index-2
differential algebraic equations

Authors: J. C. Butcher and R. P. K. Chan
Journal: Math. Comp. 67 (1998), 1001-1021
MSC (1991): Primary 65L05, 65L06, 65L20
MathSciNet review: 1464142
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In seeking suitable Runge-Kutta methods for differential algebraic equations, we consider singly-implicit methods to which are appended diagonally-implicit stages. Methods of this type are either similar to those of Butcher and Cash or else allow for the importation of a final derivative from a previous step. For these two classes, with up to three additional diagonally-implicit stages, we derive methods that satisfy appropriate order conditions for index-2 DAEs.

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

  • 1. M. Abramovitch and I. A. Stegun, Handbook of Mathematical Functions, with Formulas, Graphs and Mathematical Tables, Dover Publications, New York (1966). MR 34:8606
  • 2. K. Burrage, J. C. Butcher and F.H. Chipman, An implementation of singly-implicit Runge-Kutta methods, BIT 20 (1980), 326-340. MR 82h:65049
  • 3. K. Burrage and R.P.K. Chan, On smoothing and order reduction effects for implicit Runge-Kutta formulae, J. Comput. Appl. Math. 45 (1993), 17-27. MR 93j:65110
  • 4. J.C. Butcher, The Numerical Analysis of Ordinary Differential Equations: Runge-Kutta and General Linear Methods, J. Wiley and Sons, Chichester and New York (1987). MR 88d:65002
  • 5. J. C. Butcher, Towards efficient implementation of singly-implicit methods, ACM Trans. Math. Software 14 (1988), 68-75. MR 89b:65167
  • 6. J. C. Butcher and J.R. Cash, Towards efficient Runge-Kutta methods for stiff systems, SIAM J. Numer. Anal. 27 (1990), 753-761. MR 91a:65171
  • 7. R.P.K. Chan and P. Chartier, Gaussian symmetrizers for index-2 differential algebraic equations (unpublished notes, 1994).
  • 8. A. Erdélyi, W. Magnus, F. Oberhettinger and F.G. Tricomi, Higher Transcendental Functions, volume II, Bateman Manuscript Project, McGraw-Hill, New York, Toronto, London (1953). MR 15:419i
  • 9. E. Hairer, Ch. Lubich and M. Roche, The Numerical Solution of Differential Algebraic Systems by Runge-Kutta Methods. Lecture Notes in Math. 1409, Springer Verlag (1989). MR 91a:65178

Similar Articles

Retrieve articles in Mathematics of Computation of the American Mathematical Society with MSC (1991): 65L05, 65L06, 65L20

Retrieve articles in all journals with MSC (1991): 65L05, 65L06, 65L20

Additional Information

J. C. Butcher
Affiliation: Department of Mathematics, The University of Auckland, Auckland, New Zealand

R. P. K. Chan
Affiliation: Division of Science and Technology, Tamaki Campus, The University of Auckland, Auckland, New Zealand

Keywords: Differential algebraic systems of index 2, singly-implicit Runge-Kutta methods, diagonal extensions, Laguerre polynomials
Received by editor(s): December 9, 1994
Received by editor(s) in revised form: April 16, 1997
Additional Notes: The first author’s work was supported by the New Zealand Foundation for Research, Science and Technology.
Article copyright: © Copyright 1998 American Mathematical Society

American Mathematical Society