Asymptotic properties of the discretized pantograph equation
Result description
The paper deals with the asymptotic properties of all solutions of the delay difference equation Delta x_n=-ax_n+bx_lfloorfrac{tau(t_n)-t_0}{h}rfloor, where a>0,bneq 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
The result's identifiers
Result code in IS VaVaI
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
Asymptotic properties of the discretized pantograph equation
Original language description
The paper deals with the asymptotic properties of all solutions of the delay difference equation Delta x_n=-ax_n+bx_lfloorfrac{tau(t_n)-t_0}{h}rfloor, where a>0,bneq 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 name
Asymptotické vlastnosti diskretizované rovnice pantografu
Czech description
Tento článek se zabývá asymptotickými vlastnostmi všech řešení zpožděné diferenční rovnice Delta x_n=-ax_n+bx_lfloorfrac{tau(t_n)-t_0}{h}rfloor, where a>0,bneq 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.
Classification
Type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
IAA1163401: Limit properties of solutions of differential equations
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2005
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Studia Universitatis Babes-Bolyai Mathematica
ISSN
0252-1938
e-ISSN
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Volume of the periodical
L
Issue of the periodical within the volume
1
Country of publishing house
RO - ROMANIA
Number of pages
8
Pages from-to
77-84
UT code for WoS article
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EID of the result in the Scopus database
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Basic information
Result type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP
BA - General mathematics
Year of implementation
2005