The stability analysis of a discretized pantograph equation

Jiří Jánský; Petr Kundrát

Mathematica Bohemica (2011)

  • Volume: 136, Issue: 4, page 385-394
  • ISSN: 0862-7959

Abstract

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The paper deals with a difference equation arising from the scalar pantograph equation via the backward Euler discretization. A case when the solution tends to zero but after reaching a certain index it loses this tendency is discussed. We analyse this problem and estimate the value of such an index. Furthermore, we show that the utilized proof technique enables us to investigate some other numerical formulae, too.

How to cite

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Jánský, Jiří, and Kundrát, Petr. "The stability analysis of a discretized pantograph equation." Mathematica Bohemica 136.4 (2011): 385-394. <http://eudml.org/doc/196662>.

@article{Jánský2011,
abstract = {The paper deals with a difference equation arising from the scalar pantograph equation via the backward Euler discretization. A case when the solution tends to zero but after reaching a certain index it loses this tendency is discussed. We analyse this problem and estimate the value of such an index. Furthermore, we show that the utilized proof technique enables us to investigate some other numerical formulae, too.},
author = {Jánský, Jiří, Kundrát, Petr},
journal = {Mathematica Bohemica},
keywords = {pantograph equation; numerical solution; stability; pantograph equation; numerical solution; stability; difference equation; backward Euler discretization},
language = {eng},
number = {4},
pages = {385-394},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The stability analysis of a discretized pantograph equation},
url = {http://eudml.org/doc/196662},
volume = {136},
year = {2011},
}

TY - JOUR
AU - Jánský, Jiří
AU - Kundrát, Petr
TI - The stability analysis of a discretized pantograph equation
JO - Mathematica Bohemica
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 136
IS - 4
SP - 385
EP - 394
AB - The paper deals with a difference equation arising from the scalar pantograph equation via the backward Euler discretization. A case when the solution tends to zero but after reaching a certain index it loses this tendency is discussed. We analyse this problem and estimate the value of such an index. Furthermore, we show that the utilized proof technique enables us to investigate some other numerical formulae, too.
LA - eng
KW - pantograph equation; numerical solution; stability; pantograph equation; numerical solution; stability; difference equation; backward Euler discretization
UR - http://eudml.org/doc/196662
ER -

References

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  7. Iserles, A., 10.1016/S0168-9274(97)00027-5, Appl. Numer. Math. 24 (1997), 295-308. (1997) Zbl0880.65058MR1464730DOI10.1016/S0168-9274(97)00027-5
  8. Kundrát, P., Asymptotic properties of the discretized pantograph equation, Studia Univ. Babeş-Bolyai, Mathematica 50 (2005), 77-84. (2005) Zbl1112.39004MR2175107
  9. Kuruklis, S. A., The asymptotic stability of x n + 1 - a x n + b x n - k = 0 , J. Math. Anal. Appl. 188 (1994), 719-731. (1994) MR1305480
  10. Liu, Y., 10.1016/S0168-9274(97)00028-7, Appl. Numer. Math. 24 (1997), 309-317. (1997) Zbl0878.65065MR1464731DOI10.1016/S0168-9274(97)00028-7

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