Skip to main content

On a Research of Hybrid Methods

  • 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

Constructed hybrid methods of the high accuracy the experts examined that’s for solving integral and integro-differential equations. Using hybrid methods for solving integral equations belongs to Makroglou. Here, developing these idea, explored a more general hybrid method which is applied to solving Volterra integral equations and also constructed a concrete method with the degree p = 8. However, order of accuracy for the known corresponding methods is of level p ≤ 4.

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

Access this chapter

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. Polishuk, Y.M.: Vito Volterra. Nauka, Leningrad (1977)

    Google Scholar 

  2. Volterra, V.: Theory of functional and of integral and integro-differensial equations. Nauka, Moscow (1982)

    Google Scholar 

  3. Verlan, A.F., Sizikov, V.S.: Integral equations: methods, algorithms, programs. Naukova Dumka, Kiev (1986)

    MATH  Google Scholar 

  4. Brunner, H.: Implicit Runge-Kutta Methods of Optimal oreder for Volterra integro-differential equation. Methematics of Computation 42(165), 95–109 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  5. Lubich, C.: Runge-Kutta theory for Volterra and Abel integral equations of the second kind. Mathematics of Computation 41(163), 87–102 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  6. Makroglou, A.: Hybrid methods in the numerical solution of Volterra integro-differential equations. Journal of Numerical Analysis 2, 21–35 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  7. Mehdiyeva, G., Ibrahimov, V., Imanova, M.: On one application of hybrid methods for solving Volterra integral equations, Dubai, pp. 809–813. World Academy of Science, Engineering and Technology (2012)

    Google Scholar 

  8. Gear, C.S.: Hybrid methods for initial value problems in ordinary differential equations. SIAM, J. Numer. Anal. 2, 69–86 (1965)

    MathSciNet  MATH  Google Scholar 

  9. Butcher, J.C.: A modified multistep method for the numerical integration of ordinary differential equations. J. Assoc. Comput. Math. 12, 124–135 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  10. Hammer, P.C., Hollingsworth, J.W.: Trapezoildal methods of approximating solution of differential equations. MTAC 9, 92–96 (1955)

    MathSciNet  MATH  Google Scholar 

  11. Hairier, E., Norsett, S.P., Wanner, G.: Solving ordinary differential equations. Mir, Moscow (1990) (Russian)

    Google Scholar 

  12. Imanova, M.N.: One the multistep method of numerical solution for Volterra integral equation. Transactions Issue Mathematics and Mechanics Series of Physical-technical and Mathematical Science VI(1), 95–104 (2006)

    MathSciNet  Google Scholar 

  13. Bakhvalov, N.S.: Numerical methods. Nauka, Moscow (1973)

    Google Scholar 

  14. Mehdiyeva, G., Ibrahimov, V., Imanova, M.: On an application of the Cowell type method. News of Baku University. Series of Physico-mathematical sciences, (2), 92-99 (2010)

    Google Scholar 

  15. Imanova, M., Mehdiyeva, G., Ibrahimov, V.: Application of the Forward Jumping Method to the Solving of Volterra Integral Equation. In: Conference Proceedings NumAn 2010 Conference in Numerical Analysis, Chania, Greece, pp. 106–111 (2010)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Galina, M., Mehriban, I., Vagif, I. (2013). On a Research of Hybrid Methods. 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_44

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-41515-9_44

  • 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