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Spline Iterative Method for Pantograph Type Functional Differential Equations

  • Alexandru Mihai BicaEmail author
  • Mircea Curila
  • Sorin Curila
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

Keywords

Pantograph type equations Iterated spline method Convergence analysis 

References

  1. 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)MathSciNetCrossRefGoogle Scholar
  2. 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)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bica, A.M.: Initial value problems with retarded argument solved by iterated quadratic splines. Appl. Numer. Math. 101, 18–35 (2016)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Brunner, H.: Collocation Methods for Volterra Integral and Related Functional Differential Equations. Cambridge University Press, Cambridge (2004)CrossRefGoogle Scholar
  5. 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)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Korman, P.: Computation of displacements for nonlinear elastic beam models using monotone iterations. Internat. J. Math. Math. Sci. 11, 121–128 (1988)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Micula, G., Micula, S.: Handbook of Splines. Mathematics and its Applications, vol. 462. Kluwer Academic Publishers, Dordrecht (1999).  https://doi.org/10.1007/978-94-011-5338-6CrossRefzbMATHGoogle Scholar
  8. 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)CrossRefGoogle Scholar
  9. 9.
    Stoer, J., Bulirsch, R.: Introduction to Numerical Analysis. Texts in Applied Mathematics, 2nd edn. Springer, New York (1993).  https://doi.org/10.1007/978-1-4757-2272-7CrossRefzbMATHGoogle Scholar
  10. 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

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUniversity of OradeaOradeaRomania
  2. 2.Department of Environmental ProtectionUniversity of OradeaOradeaRomania
  3. 3.Department of Electronics and TelecommunicationsUniversity of OradeaOradeaRomania

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