Skip to main content
SpringerLink
Log in

Quadrature Formula with Five Nodes for Functions with a Boundary Layer Component

  • Conference paper
Numerical Analysis and Its Applications (NAA 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8236))

Included in the following conference series:

Abstract

Quadrature formula for one variable functions with a boundary layer component is constructed and studied. It is assumed that the integrand can be represented as a sum of regular and boundary layer components. The boundary layer component has high gradients, therefore an application of Newton-Cotes quadrature formulas leads to large errors. An analogue of Newton-Cotes rule with five nodes is constructed. The error of the constructed formula does not depend on gradients of the boundary layer component. Results of numerical experiments are presented.

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. Berezin, I.S., Zhidkov, N.P.: Computing Methods. Nauka, Moskow (1966) (in Russian)

    Google Scholar 

  2. Bakhvalov, N.S.: Numerical Methods. Nauka, Moskow (1975) (in Russian)

    Google Scholar 

  3. Zadorin, A.I., Zadorin, N.A.: Quadrature formulas for functions with a boundary-layer component. Comput. Math. Math. Phys. 51(11), 1837–1846 (2011)

    Article  MathSciNet  Google Scholar 

  4. Miller, J.J.H., O’Riordan, E., Shishkin, G.I.: Fitted Numerical Methods for Singular Perturbation Problems. World Scientific, Singapore (1996)

    MATH  Google Scholar 

  5. Zadorin, A.I.: Method of interpolation for a boundary layer problem. Sib. J. of Numer. Math. 10(3), 267–275 (2007) (in Russian)

    Google Scholar 

  6. Zadorin, A.I.: Interpolation Method for a Function with a Singular Component. In: Margenov, S., Vulkov, L.G., Waśniewski, J. (eds.) NAA 2008. LNCS, vol. 5434, pp. 612–619. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  7. Zadorin, A.I., Zadorin, N.A.: Spline interpolation on a uniform grid for functions with a boundary-layer component. Comput. Math. Math. Phys. 50(2), 211–223 (2010)

    Article  MathSciNet  Google Scholar 

  8. Zadorin, A.I.: Spline interpolation of functions with a boundary layer component. Int. J. Numer. Anal. Model., series B 2(2-3), 562–579 (2011)

    MathSciNet  Google Scholar 

  9. Vulkov, L.G., Zadorin, A.I.,: Two-grid algorithms for an ordinary second order equation with exponential boundary layer in the solution. Int. J. Numer. Anal. Model. 7(3), 580–592 (2010)

    MathSciNet  MATH  Google Scholar 

  10. Dahlquist, G., Bjorck, A.: Numerical Methods in Scientific Computing, vol. 1. SIAM, Philadelphia (2008)

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Omsk Filial of Sobolev Mathematics Institute SB RAS, Pevtsova 13, Omsk, 644099, Russia

    Alexander Zadorin & Nikita Zadorin

Authors
  1. Alexander Zadorin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nikita Zadorin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Information and Communication Technlogies, Bulgarian Academy of Sciences, Acad. G. Bonchev, Bl25A, 1113, Sofia, Bulgaria

    Ivan Dimov

  2. Department of Applied Analysis, Pázm\’{a}ny P\’{e}ter s\’{e}t\’{a}ny 1/C,, Eötvös Loránd University, 1117, Budapest, Hungary

    István Faragó

  3. University of Rousse, 8 Studentska Str.,, 7017, Rousse, Bulgaria

    Lubin Vulkov

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Zadorin, A., Zadorin, N. (2013). Quadrature Formula with Five Nodes for Functions with a Boundary Layer Component. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Numerical Analysis and Its Applications. NAA 2012. Lecture Notes in Computer Science, vol 8236. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41515-9_62

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-41515-9_62

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-41514-2

  • Online ISBN: 978-3-642-41515-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation