Skip to main content
SpringerLink
Log in

Asymptotic expansions of the global error for the implicit midpoint rule (stiff case)

Asymptotische Entwicklungen des globalen Fehlers der impliziten Mittelpunktsregel (steifer Fall)

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

Abstract

In this contribution an asymptotic expansion of the global error for the box scheme (implicit midpoint rule) in a stiff case on a highly non-uniform mesh will be discussed. The details and the proofs may be found in [7].

Zusammenfassung

In diesem Beitrag wird eine asymptotische Entwicklung für das Box-Schema (implizite Mittelpunktsregel) im Fall einer steifen Gleichung auf einem stark ungleichmäßigen Gitter diskutiert. Details und Beweise finden sich in [7].

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. Ascher, U., Weiss, R.: Collocation for singular perturbation problems II: linear first order systems without turning points. SIAM J. Numer. Anal. (to appear).

  2. Pereyra, V.: Accelerating the convergence of discretization algorithms. SIAM J. Numer. Anal.4, 508–533 (1967).

    Article  Google Scholar 

  3. Pereyra, V.: PASVA3: An adaptive finite difference FORTRAN program for first order NLOB's. In: Codes for BVP's in ODE's (Lecture Notes in Computer Science, Vol. 76). Berlin-Heidelberg-New York: Springer 1979.

    Google Scholar 

  4. Skeel, R. D.: A theoretical framework for proving accuracy results for deferred corrections. SIAM J. Numer. Anal.19, 171–196 (1982).

    Article  Google Scholar 

  5. Stetter, H. J.: Asymptotic expansions of the error of discretization algorithms for non-linear functional equations. Numer. Math.7, 18–31 (1965).

    Article  Google Scholar 

  6. Stetter, H. J.: The defect correction principle and discretization methods. Numer. Math.29, 425–443 (1978).

    Article  Google Scholar 

  7. Veldhuizen, M. van: Asymptotic expansion of the global error of the box scheme in a stiff case. Report Dept. Math. and Comp. Science VU, no. 251 (1984).

  8. Weiss, R.: An analysis of the box and trapezoidal schemes for linear singularly perturbed boundary value problems. Manuscript (1982).

  9. Zadunaisky, P. E.: On the estimation of errors propagated in the numerical integration of ordinary differential equations. Numer. Math.27, 21–40 (1976).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Free University, P.O. Box 7161, NL-1007 MC, Amsterdam, The Netherlands

    M. van Veldhuizen

Authors
  1. M. van Veldhuizen
    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

van Veldhuizen, M. Asymptotic expansions of the global error for the implicit midpoint rule (stiff case). Computing 33, 185–192 (1984). https://doi.org/10.1007/BF02240190

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02240190

AMS Subject Classification

Key words

Search

Navigation