Skip to main content
SpringerLink
Log in

On the computational aspects of Rosenbrock procedures with built-in error estimates for stiff systems

  • Part II Numerical Mathematics
  • Published:
BIT Numerical Mathematics Aims and scope Submit manuscript

Abstract

A third orderA-stable Rosenbrock method with built-in error estimate is developed by modifying an idea of J. R. Cash. Comparative tests are presented.

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

Similar content being viewed by others

References

  1. J. D. Lambert,Computational Methods in Ordinary Differential Equations, J. Wiley and Sons, New York, (1973).

    Google Scholar 

  2. J. R. Cash,Semi-implicit Runge-Kutta procedures with error estimates for the numerical integration of stiff systems of ordinary differential equations, J. ACM, 23 (1976), 455–460.

    Google Scholar 

  3. T. D. Bui, Errata and Comments on the preceding paper, J. ACM, 24 (1977), 623.

    Google Scholar 

  4. T. D. Bui,On an L-Stable method for stiff differential equations, Inf. Proc. Letters, 6 (1977), 158–161.

    Google Scholar 

  5. C. F. Haines,Implicit integration processes with error estimates for the numerical solution of differential equations, Computer J., 12 (1968), 183–187.

    Google Scholar 

  6. W. H. Enright, T. E. Hull and B. Lindberg,Comparing numerical methods for stiff systems of ODE's, BIT, 15 (1975), 10–48.

    Google Scholar 

  7. J. R. Cash and C. B. Liem,On the computational aspects of semi-implicit Runge-Kutta methods, Comput. J., 21 (1978), 363–365.

    Google Scholar 

  8. D. Calahan,A stable accurate method for the numerical integration of nonlinear systems, Proc. IEEE, 56 (1968), 744.

    Google Scholar 

  9. H. H. Rosenbrock,Some general implicit processes for the numerical solution of differential equations, Comput. J., 5 (1963), 329–330.

    Google Scholar 

  10. A. C. Hindmarsh,GEAR: Ordinary differential equation system solver, LRL Rep. UCID-30001 Revision 3, December, (1974).

  11. C. W. Gear,Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, N. J., (1971), 76–84.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Concordia University, Montréal, Québec, Canada

    T. D. Bui & S. W. H. Poon

Authors
  1. T. D. Bui
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. W. H. Poon
    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

Bui, T.D., Poon, S.W.H. On the computational aspects of Rosenbrock procedures with built-in error estimates for stiff systems. BIT 21, 168–174 (1981). https://doi.org/10.1007/BF01933161

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01933161

Keywords

Search

Navigation