Skip to main content
SpringerLink
Log in

Numerical Method for a Nonlinear Singularly Perturbed Interior Layer Problem

  • Conference paper
  • First Online:
Book cover BAIL 2010 - Boundary and Interior Layers, Computational and Asymptotic Methods

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 81))

Abstract

Nonlinear singularly perturbed interior layer problems are examined. Numerical results are presented for a numerical method consisting of a monotone scheme on a Shishkin mesh refined around the approximate location of the interior layer.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover 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. L. Abrahamsson, S. Osher, Monotone Difference Schemes for Singular Perturbation Problems, SIAM J. Numer. Anal., 19, (5), 1982, 979–992.

    Article  MathSciNet  MATH  Google Scholar 

  2. S.R. Bernfield and V. Lakshmikantham, An Introduction to Nonlinear Boundary Value Problems. Academic Press, New York, (1974).

    Google Scholar 

  3. P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O‘Riordan and G.I. Shishkin, Robust Computational Techniques for Boundary Layers, Chapman and Hall/CRC, Boca Raton, FL. (2000).

    Google Scholar 

  4. P.A. Farrell, E. O’Riordan and G.I. Shishkin, A class of singularly perturbed semilinear differential equations with interior layers, Mathematics of Computation, 74, (252), 2005, 1759–1776.

    Article  MathSciNet  MATH  Google Scholar 

  5. F.A. Howes Boundary-interior layer interactions in nonlinear singular perturbation theory, Memoirs of the American Mathematical Society, 15, (203), 1978.

    Google Scholar 

  6. G.S. Ladde, V. Lakshmikantham and A.S. Vatsala Monotone Iterative Techniques for Nonlinear Differential Equations. Pitman Publishing, London, (1985).

    Google Scholar 

  7. E. O’Riordan and J. Quinn Parameter-uniform numerical methods for some linear and nonlinear singularly perturbed convection diffusion boundary turning point problems, Dublin City University, Preprint MS-10-02 (2010) (to appear in BIT).

    Google Scholar 

  8. G.I. Shishkin, Difference approximation of the dirichlet problem for a singularly perturbed quasilinear parabolic equation in the presence of a transition layer, Russian Acad. Sci. Dokl. Math., 48, (2), 1994, 346–352.

    MathSciNet  Google Scholar 

Download references

Acknowledgements

This research was supported by the Irish Research Council for Science, Engineering and Technology.

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Dublin City University, Dublin, Ireland

    E. O’Riordan & J. Quinn

Authors
  1. E. O’Riordan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Quinn
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. O’Riordan .

Editor information

Editors and Affiliations

  1. , Dept. of Applied Mathematics, University of Zaragoza, María de Luna 3, Zaragoza, 50018, Spain

    Carmelo Clavero

  2. , Dept. of Applied Mathematics, University of Zaragoza, María de Luna 3, Zaragoza, 50018, Spain

    José Luis Gracia

  3. , Dept. of Applied Mathematics, University of Zaragoza, Pedro Cerbuna 12, Zaragoza, 50009, Spain

    Francisco J. Lisbona

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

O’Riordan, E., Quinn, J. (2011). Numerical Method for a Nonlinear Singularly Perturbed Interior Layer Problem. In: Clavero, C., Gracia, J., Lisbona, F. (eds) BAIL 2010 - Boundary and Interior Layers, Computational and Asymptotic Methods. Lecture Notes in Computational Science and Engineering, vol 81. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19665-2_20

Download citation

Publish with us

Policies and ethics

Search

Navigation