Skip to main content
SpringerLink
Log in

Collocation Methods for Boundary Value Problems with an Essential Singularity

  • Conference paper
Large-Scale Scientific Computing (LSSC 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2907))

Included in the following conference series:

Abstract

We investigate collocation methods for the efficient solution of singular boundary value problems with an essential singularity. We give numerical evidence that this approach indeed yields high order solutions. Moreover, we discuss the issue of a posteriori error estimation for the collocation solution. An estimate based on the defect correction principle, which has been successfully applied to problems with a singularity of the first kind, is less robust with respect to an essential singularity than a classical strategy based on mesh halving.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Auzinger, W., Kneisl, G., Koch, O., Weinmüller, E.: A collocation code for boundary value problems in ordinary differential equations. Numer. Algorithms (to appear), Also available as ANUM Preprint Nr. 18/01 at http://www.math.tuwien.ac.at/~inst115/preprints.htm

  2. Auzinger, W., Koch, O., Petrickovic, J., Weinmüller, E.: The numerical solution of boundary value problems with an essential singularity. Techn. Rep. ANUM Preprint Nr. 3/03, Inst. for Appl. Math. and Numer. Anal., Vienna Univ. of Technology, Austria (2003), Available at http://www.math.tuwien.ac.at/~inst115/preprints.htm

  3. Auzinger, W., Koch, O., Weinmüller, E.: Efficient collocation schemes for singular boundary value problems. Numer. Algorithms 31, 5–25 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  4. Auzinger, W., Koch, O., Weinmüller, E.: Analysis of a new error estimate for collocation methods applied to singular boundary value problems. SIAM J. Numer. Anal. (submitted to), Also available as ANUM Preprint Nr. 13/02 at http://www.math.tuwien.ac.at/~inst115/preprints.htm

  5. Bergström, A.: Electromagnetic theory of strong interaction. Phys. Rev. D 8, 4394–4402 (1973)

    Article  Google Scholar 

  6. Boor, C.D., Swartz, B.: Collocation at Gaussian points. SIAM J. Numer. Anal. 10, 582–606 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  7. Hoog, F.D., Weiss, R.: The numerical solution of boundary value problems with an essential singularity. SIAM J. Numer. Anal. 16, 637–669 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  8. Hoog, F.D., Weiss, R.: On the boundary value problem for systems of ordinary differential equations with a singularity of the second kind. SIAM J. Math. Anal. 11, 41–60 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  9. Lentini, M., Keller, H.: Boundary value problems on semi-infinite intervals and their numerical solution. SIAM J. Numer. Anal. 17, 577–604 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  10. Markowich, P.: Asymptotic analysis of von Karman flows. SIAM J. Appl. Math. 42, 549–557 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  11. Schlichting, H.: Boundary Layer Theory. McGraw-Hill, New York (1968)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Applied Mathematics and Numerical Analysis, Vienna University of Technology, Austria

    Winfried Auzinger, Othmar Koch & Ewa Weinmüller

Authors
  1. Winfried Auzinger
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Othmar Koch
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ewa Weinmüller
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev, Bl. 25A, 1113, Sofia, Bulgaria

    Ivan Lirkov

  2. Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 25-A, 1113, Sofia, Bulgaria

    Svetozar Margenov

  3. Informatics & Mathematical Modeling, Technical University of Denmark, DK-2800, Lyngby, Denmark

    Jerzy Waśniewski

  4. Center of Applied Mathematics and Informatics, University of Rousse, 7017, Rousse, Bulgaria

    Plamen Yalamov

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Auzinger, W., Koch, O., Weinmüller, E. (2004). Collocation Methods for Boundary Value Problems with an Essential Singularity. In: Lirkov, I., Margenov, S., Waśniewski, J., Yalamov, P. (eds) Large-Scale Scientific Computing. LSSC 2003. Lecture Notes in Computer Science, vol 2907. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24588-9_39

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-24588-9_39

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21090-0

  • Online ISBN: 978-3-540-24588-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation