Skip to main content
SpringerLink
Log in

A reliable rosenbrock integrator for stiff differential equations

Ein verläßliches Rosenbrock-Programm für steife Differentialgleichungen

  • Short Communications
  • Published:
Computing Aims and scope Submit manuscript

Abstract

This note points out that the reliability of step-by-step integrators for ordinary differential equations can be increased considerably by a simple trick. We incorporated this idea into a program based on an A-stable Rosenbrock formula. This program comprises about 100 statements only and gives good numerical results.

Zusammenfassung

Es wird gezeigt, daß die Sicherheit eines Programmes für gewöhnliche Differentialgleichungen durch einen einfachen Trick wesentlich erhöht werden kann. Mit Hilfe dieser Idee und einer A-stabilen Rosenbrock-Formel haben wir ein kleines Programm geschrieben, welches gute numerische Resultate liefert.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Dahlquist, G.: A special stability criterion for linear multistep methods. BIT3, 22–43 (1963).

    Google Scholar 

  2. Enright, W., Hull, T. E., Lindberg, B.: Comparing numerical methods for stiff systems of ODE's. BIT15, 10–48 (1975).

    Google Scholar 

  3. Field, R. J., Noyes, R. M.: Oscillations in chemical systems IV. Limit cycle behavior in a model of a real chemical reaction. J. Chem. Phys.60, 1877 (1974).

    Google Scholar 

  4. Hindmarsh, A. C., Byrne, G. D.: Applications of EPISODE, in: Numerical methods for differential systems (Lapidus, Schiesser, eds.). 1976.

  5. Kaps, P., Rentrop, P.: Generalized Runge Kutta methods of order four with step size control for stiff ODE's. Numer. Math.33, 55–68 (1979).

    Google Scholar 

  6. Kaps, P., Wanner, G.: A study of Rosenbrock type methods of high order. Submitted to Numer. Math.

  7. Nørsett, S. P., Wolfbrandt, A.: Order conditions for Rosenbrock type methods. Numer. Math.32, 1–15 (1979).

    Google Scholar 

  8. Schäfer, E.: A new approach to explain the “high irradiance responses” of photomorphogenesis on the basis of phytochrome. J. Math. Biol.2, 41 (1975).

    Google Scholar 

  9. Wolfbrandt, A.: A study of Rosenbrock processes with respect to order conditions and stiff stability. Thesis, Chalmers University of Technology, Göteborg, Sweden, 1977.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fakultät für Biologie, Universität Freiburg i. Br., Schänzlestrasse 1, D-7800, Freiburg i. Br., Federal Republic of Germany

    B. A. Gottwald

  2. Section de Mathématiques, Case postale 124, CH-1211, Genève 24, Switzerland

    G. Wanner

Authors
  1. B. A. Gottwald
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Wanner
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gottwald, B.A., Wanner, G. A reliable rosenbrock integrator for stiff differential equations. Computing 26, 355–360 (1981). https://doi.org/10.1007/BF02237954

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02237954

Keywords

Search

Navigation