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On a linear difference equation with several infinite lags

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Języki publikacji
EN
Abstrakty
EN
This paper deals with asymptotic properties of the solutions of a variable order linear difference equation. As the main result, we derive the effective asymptotic estimate valid for all solutions of this equation. Moreover, we are going to discuss some consequences of this theoretical result, especially with respect to the numerical analysis of the multi-pantograph differential equation.
Rocznik
Tom
Strony
19--28
Opis fizyczny
Bibliogr. 17 poz.
Twórcy
autor
  • Institute of Mathematics Brno University of Technology Technická 2 CZ-61669 Brno, Czech Republic, cermak.j@fme.vutbr.cz
Bibliografia
  • [1] Agarwal R.P., Pituk M., Asymptotic expansions for higher-order scalar difference equations, Advances in Difference Equations, 2007(2007), 1-12.
  • [2] Bellen A., Zennaro M., Numerical Methods For Delay Differential Equations, Numerical Mathematics and Scientific Computation, The Clarendon Press, Oxford University Press, New York, 2003.
  • [3] Berezansky L., Braverman E., Exponential stability of difference equations with several delays: Recursive approach, Advances in Difference Equations, 2009(2009), 1-13.
  • [4] Buhmann M.D., Iserles A., Stability of the discretized pantograph differential equation, Math. Comp., 60(1993), 575-589.
  • [5] Čermćak J., Asymptotic estimation for functional differential equations with several delays, Archivum Math. (Brno), 35(1999), 337-345.
  • [6] Čermćak J., JČnskáý J., On the asymptotics of the trapezoidal rule for the pantograph equation, Math. Comp., 78(2009), 2107-2126.
  • [7] Diblík J., Khusainov D.Ya., Šmarda Z., Construction of the general solution of planar linear discrete systems with constant coefficients and weak delay, Advances in Difference Equations, 2009(2009), 1-18.
  • [8] Elaydi S., Asymptotics for linear difference equations I: Basic theory, J. Difference Equ. and Appl., 5(1999), 563-589.
  • [9] Farkas G., On asymptotics of solutions of Poincaré difference systems, J. Difference Equ. Appl., 7(2001), 183-191.
  • [10] Györi I., Pituk M., Asymptotic formulae for the solutions of a linear delay difference equations, J. Math. Anal. Appl., 195(1995), 376-392.
  • [11] Iserles A., Numerical analysis of delay differential equations with variable delays, Ann. Numer. Math., 1(1994), 133-152.
  • [12] Kuang J., Cong Y., Stability of Numerical Methods For Delay Differential Equations, Science Press, Beijing, 2005.
  • [13] Liu Y., On the θ-method for delay differential equations with infinite lag, J. Comput. Appl. Math., 71(1996), 177-190.
  • [14] Liu M.Z., Li D., Properties of analytic solution and numerical solution of multi-pantograph equation, Appl. Math. Comput., 155(2004), 853-871.
  • [15] Liu M.Z., Yang Z.W., Hu G.D., Asymptotical stability of numerical methods with constant stepsize for the pantograph equations, BIT, 45(2005), 743-759.
  • [16] Péics H., On the asymptotic behaviour of difference equations with continuous argument, Ser. A. Math. Anal., 9(2002), 257-273.
  • [17] Qiu L., Mistsui T., Kuang J.X., The numerical stability of the θ-methods for delay differential equations with many variable delays, J. Computational Mathematics, 17(5)(1999), 523-532.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPP3-0002-0078
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