Publication detail

Asymptotic properties of the discretized pantograph equation

KUNDRÁT, P.

Czech title

Asymptotické vlastnosti diskretizované rovnice pantografu

English title

Asymptotic properties of the discretized pantograph equation

Type

journal article - other

Language

en

Original abstract

The paper deals with the asymptotic properties of all solutions of the delay difference equation \Delta x_n=-ax_n+bx_\lfloor\frac{\tau(t_n)-t_0}{h}\rfloor, where a>0,b\neq 0 are reals. This equation represents the discretization of the corresponding delay differential equation. Our aim is to show the resemblance in the asymptotic bounds of solutions of the discrete and continuous equation and discuss some numerical problems connected with this investigation.

Czech abstract

Tento článek se zabývá asymptotickými vlastnostmi všech řešení zpožděné diferenční rovnice \Delta x_n=-ax_n+bx_\lfloor\frac{\tau(t_n)-t_0}{h}\rfloor, where a>0,b\neq 0 are reals. Tato rovnice je diskretizací odpovídající zpožděné diferenciální rovnice. Cílem je ukázat souvislosti mezi asymptotickými odhady řešení diskrétní a spojité rovnice a následně diskutovat některé problémy numerické analýzy spojené s tímto vyšetřováním.

English abstract

The paper deals with the asymptotic properties of all solutions of the delay difference equation \Delta x_n=-ax_n+bx_\lfloor\frac{\tau(t_n)-t_0}{h}\rfloor, where a>0,b\neq 0 are reals. This equation represents the discretization of the corresponding delay differential equation. Our aim is to show the resemblance in the asymptotic bounds of solutions of the discrete and continuous equation and discuss some numerical problems connected with this investigation.

Keywords in English

Differential equation, difference equation

RIV year

2005

Released

01.01.2005

ISSN

0252-1938

Journal

Studia Universitatis Babes-Bolyai Mathematica

Volume

L

Number

1

Pages count

8

BIBTEX


@article{BUT42431,
  author="Petr {Tomášek},
  title="Asymptotic properties of the discretized pantograph equation",
  journal="Studia Universitatis Babes-Bolyai Mathematica",
  year="2005",
  volume="L",
  number="1",
  month="January",
  issn="0252-1938"
}