Applications of differential transform to boundary value problems for delayed differential equations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26620%2F20%3APU138048" target="_blank" >RIV/00216305:26620/20:PU138048 - isvavai.cz</a>

Výsledek na webu

<a href="https://aip.scitation.org/doi/abs/10.1063/5.0026599" target="_blank" >https://aip.scitation.org/doi/abs/10.1063/5.0026599</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1063/5.0026599" target="_blank" >10.1063/5.0026599</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Applications of differential transform to boundary value problems for delayed differential equations

Popis výsledku v původním jazyce

An application of the differential transformation is proposed in this paper which is convenient for finding approximate solutions to boundary value problems for functional differential equations. We focus on two-point boundary value problem for equations with constant delays. Delayed differential equation is turned into an ordinary differential equation using the method of steps. The ordinary differential equation is transformed into recurrence relation in one variable. Based on the structure of the studied boundary value problem, the solution to the recurrence relation depends on one real parameter. Using the boundary conditions leads to an equation with the unknown parameter as the single variable which occurs generally in infinitely many terms. Approximate solution has the form of a Taylor polynomial. Coefficients of the polynomial are determined by solving the recurrence relation and a truncated equation with respect to the unknown parameter. Particular steps of the algorithm are demonstrated in an example of two-point boundary value problem for a differential equation with one constant delay.

Název v anglickém jazyce

Applications of differential transform to boundary value problems for delayed differential equations

Popis výsledku anglicky

An application of the differential transformation is proposed in this paper which is convenient for finding approximate solutions to boundary value problems for functional differential equations. We focus on two-point boundary value problem for equations with constant delays. Delayed differential equation is turned into an ordinary differential equation using the method of steps. The ordinary differential equation is transformed into recurrence relation in one variable. Based on the structure of the studied boundary value problem, the solution to the recurrence relation depends on one real parameter. Using the boundary conditions leads to an equation with the unknown parameter as the single variable which occurs generally in infinitely many terms. Approximate solution has the form of a Taylor polynomial. Coefficients of the polynomial are determined by solving the recurrence relation and a truncated equation with respect to the unknown parameter. Particular steps of the algorithm are demonstrated in an example of two-point boundary value problem for a differential equation with one constant delay.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/LQ1601" target="_blank" >LQ1601: CEITEC 2020</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2019 (ICNAAM-2019)

ISBN

978-0-7354-4025-8

ISSN

0094-243X

e-ISSN

—

Počet stran výsledku

4

Strana od-do

„340011-1“-„340011-4“

Název nakladatele

American Institute of Physics

Místo vydání

Melville (USA)

Místo konání akce

hotel Sheraton, Ixia, Rhodos

Datum konání akce

23. 9. 2019

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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