Skip to main content
SpringerLink
Log in

Numerical solution of a singular perturbation problem with turning points

  • Conference paper
  • First Online:
Equadiff 82

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1017))

Abstract

Nonlinear singular perturbation problems with turning points are discretized on a uniform mesh. The scheme is second order on smooth solutions. Unique solubility of the difference equations is investigated.

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 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.00
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. Howes, F.A.: Boundary-interior layer interactions in nonlinear singular perturbation theory. Memoirs AMS, No. 203 (1978).

    Google Scholar 

  2. Lorenz, J.: Zur Theorie und Numerik von Differenzenverfahren für singuläre Störungen. Habilitationsschrift, Universität Konstanz, 1980.

    Google Scholar 

  3. Lorenz, J.: Nonlinear singular perturbation problems and the Engquist-Osher difference scheme. University of Nijmegen, Report 8115, 1981.

    Google Scholar 

  4. Lorenz, J.: Nonlinear boundary value problems with turning points and properties of difference schemes. To appear in: Proc. Conf. Singuläre Störungstheorie mit Anwendungen, Oberwolfach 1981, Springer Lecture Notes.

    Google Scholar 

  5. Moré, J., Rheinboldt, W.: On P-and S-functions and related classes of n-dimensional nonlinear mappings. Lin. Alg. Appl. 6, 45–68 (1973).

    Article  MathSciNet  MATH  Google Scholar 

  6. Ortega, J.M., Rheinboldt, W.C.: Iterative solution of nonlinear equations in several variables. Academic Press, New York, London, 1970.

    MATH  Google Scholar 

  7. Osher, S.: Nonlinear singular perturbation problems and one sided difference schemes. SIAM J. Num. Anal. 18, 129–144 (1981).

    Article  MathSciNet  MATH  Google Scholar 

  8. Osher, S.: Numerical solution of singular perturbation problems and hyperbolic systems of conservation laws. In: Analytical and numerical approaches to asymptotic problems in analysis. S. Axelsson, L.S. Frank, A. van der Sluis (eds.), North-Holland, 1981, pp. 179–204.

    Google Scholar 

  9. Stephens, A.B., Shubin, G.R.: Multiple solutions and bifurcation of finite difference approximations to some steady problems of fluid dynamics. SIAM J. Sci. Stat. Comput. 2, 404–415 (1981).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fakultät für Mathematik der, Universität Konstanz, D775, Konstanz, Germany

    J. Lorenz

Authors
  1. J. Lorenz
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

H. W. Knobloch Klaus Schmitt

Rights and permissions

Reprints and permissions

Copyright information

© 1983 Springer-Verlag

About this paper

Cite this paper

Lorenz, J. (1983). Numerical solution of a singular perturbation problem with turning points. In: Knobloch, H.W., Schmitt, K. (eds) Equadiff 82. Lecture Notes in Mathematics, vol 1017. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0103269

Download citation

  • DOI: https://doi.org/10.1007/BFb0103269

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12686-7

  • Online ISBN: 978-3-540-38678-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation