Skip to main content
SpringerLink
Log in
Book cover

International Conference on Finite Difference Methods

FDM 2018: Finite Difference Methods. Theory and Applications pp 159–166Cite as

Spline Iterative Method for Pantograph Type Functional Differential Equations

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11386))

Abstract

Initial value problems and two-point boundary value problems for nonlinear pantograph type differential equations are investigated by presenting a new iterative numerical method based on constructing a sequence of splines that converges to the solution. The convergence of the method was proved by providing an error estimate and is tested on some numerical experiments.

This is a preview of subscription content, 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 EPUB and 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

Learn about institutional subscriptions

References

  1. Agarwal, R.P., Chow, Y.M.: Finite-difference methods for boundary-value problems of differential equations with deviating arguments. Comput. Math. Appl. 12A, 1143–1153 (1986)

    Article  MathSciNet  Google Scholar 

  2. Bica, A.M., Curila, M., Curila, S.: Two-point boundary value problems associated to functional differential equations of even order solved by iterated splines. Appl. Numer. Math. 110, 128–147 (2016)

    Article  MathSciNet  Google Scholar 

  3. Bica, A.M.: Initial value problems with retarded argument solved by iterated quadratic splines. Appl. Numer. Math. 101, 18–35 (2016)

    Article  MathSciNet  Google Scholar 

  4. Brunner, H.: Collocation Methods for Volterra Integral and Related Functional Differential Equations. Cambridge University Press, Cambridge (2004)

    Book  Google Scholar 

  5. Brunner, H.: Recent advances in the numerical analysis of Volterra functional differential equations with variable delays. J. Comput. Appl. Math. 228, 524–537 (2009)

    Article  MathSciNet  Google Scholar 

  6. Korman, P.: Computation of displacements for nonlinear elastic beam models using monotone iterations. Internat. J. Math. Math. Sci. 11, 121–128 (1988)

    Article  MathSciNet  Google Scholar 

  7. Micula, G., Micula, S.: Handbook of Splines. Mathematics and its Applications, vol. 462. Kluwer Academic Publishers, Dordrecht (1999). https://doi.org/10.1007/978-94-011-5338-6

    Book  MATH  Google Scholar 

  8. Ockendon, J.R., Tayler, A.B.: The dynamics of a current collection system for an electric locomotive. Proc. Roy. Soc. Lond. A 322, 447–468 (1971)

    Article  Google Scholar 

  9. Stoer, J., Bulirsch, R.: Introduction to Numerical Analysis. Texts in Applied Mathematics, 2nd edn. Springer, New York (1993). https://doi.org/10.1007/978-1-4757-2272-7

    Book  MATH  Google Scholar 

  10. Wazwaz, A.-M., Raja, M.A.Z., Syam, M.I.: Reliable treatment for solving boundary value problems of pantograph delay differential equation. Rom. Rep. Phys. 69, 102 (2017)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Oradea, Universitatii Str. no. 1, 410087, Oradea, Romania

    Alexandru Mihai Bica

  2. Department of Environmental Protection, University of Oradea, Oradea, Romania

    Mircea Curila

  3. Department of Electronics and Telecommunications, University of Oradea, Oradea, Romania

    Sorin Curila

Authors
  1. Alexandru Mihai Bica
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mircea Curila
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sorin Curila
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alexandru Mihai Bica .

Editor information

Editors and Affiliations

  1. IICT, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Dimov

  2. Eötvös Loránd University, Budapest, Hungary

    István Faragó

  3. University of Rousse, Rousse, Bulgaria

    Lubin Vulkov

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Bica, A.M., Curila, M., Curila, S. (2019). Spline Iterative Method for Pantograph Type Functional Differential Equations. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Finite Difference Methods. Theory and Applications. FDM 2018. Lecture Notes in Computer Science(), vol 11386. Springer, Cham. https://doi.org/10.1007/978-3-030-11539-5_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-11539-5_16

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-11538-8

  • Online ISBN: 978-3-030-11539-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation