Skip to main content
SpringerLink
Log in

Asymptotic stability and discretization on an infinite interval

Asymptotische Stabilität und Diskretisierung auf einem unendlichen Intervall

  • Published:
Computing Aims and scope Submit manuscript

Abstract

By imposing some conditions on the discrete dynamical systems generated by one step discretization methods, we construct some non linear one step methods of the first and second order, which turn out to beA-stable orL-stable according to the current definitions. Numerical experiments are carried out on some common stiff test problems, confirming the validity of the methods.

Zusammenfassung

Indem wir den aus den One-Step-Diskretierungsmethoden entstandenen dynamischen Systemen einige Bedingungen auferlegen, konstruieren wir einige nichtlineare One-Step-Methoden von erster und zweiter Ordnung, die nach der allgemeinen BezeichnungA-stabil oderL-stabil sind. Zahlenergebnisse an einigen „steifen” Test-Problemen, die vorgelegt werden, bestätigen die Brauchbarkeit dieser Methoden.

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. Lambert, J. D.: Computational Methods in Ordinary Differential Equations. Wiley 1973.

  2. Lambert, J. D.: Two unconventional classes of methods for Stiff Systems, in: Stiff Differential Systems (Willoughby, R. A., ed.). Plenum. 1974.

  3. Enright, W. E.: Second derivative multistep methods for Stiff Ordinary differential equations. SIAM JNA1973, 321–331.

  4. Liniger, W., Willoughby, R. A.: Efficient Integration methods for Stiff Systems of Ordinary Differential Equations. SIAM JNA7, 47–66 (1970).

    Google Scholar 

  5. Liniger, W., Odeh, F.:A-stable, Accurate Averaging of Multistep Methods for Stiff Differential Equations. IBM JAE16, 335–348 (1972).

    Google Scholar 

  6. Stetter, H. J.: Stability of discretizations on infinite intervals. Conference on Applications of Num. Analysis (1971), pp. 207–222. Berlin-Heidelberg-New York: Springer.

    Google Scholar 

  7. Bathia, N. P., Szego, G. P.: Stability Theory for Dynamical Systems. Berlin-Heidelberg-New York: Springer 1970.

    Google Scholar 

  8. Nevanlinna, O., Sipila, A. H.: A non existence theorem for explicitA-stable methods. Mathematics of computation28, 128, 1053–1055 (1974).

    Google Scholar 

  9. Sansoni, G., Conti, R.: Non linear differential equations. Macmillan 1964.

  10. Marchetti, L., Negrini, P., Salvadori, L., Scalia, M.: Liapunov direct method in approaching biforcation problems. (To be published in Annali di Matematica).

Download references

Author information

Authors and Affiliations

  1. Centro Ricerche IBM, Via Cardassi 3, Bari, Italy

    D. Trigiante

Authors
  1. D. Trigiante
    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

Trigiante, D. Asymptotic stability and discretization on an infinite interval. Computing 18, 117–129 (1977). https://doi.org/10.1007/BF02243621

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02243621

Keywords

Search

Navigation