Differential transform algorithm for functional differential equations with time-dependent delays

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F70883521%3A28140%2F20%3A63525249" target="_blank" >RIV/70883521:28140/20:63525249 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216305:26620/20:PU136085

Výsledek na webu

<a href="https://www.hindawi.com/journals/complexity/2020/2854574/" target="_blank" >https://www.hindawi.com/journals/complexity/2020/2854574/</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1155/2020/2854574" target="_blank" >10.1155/2020/2854574</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Differential transform algorithm for functional differential equations with time-dependent delays

Popis výsledku v původním jazyce

An algorithm using the differential transformation which is convenient for finding numerical solutions to initial value problems for functional differential equations is proposed in this paper. We focus on retarded equations with delays which in general are functions of the independent variable. The delayed differential equation is turned into an ordinary differential equation using the method of steps. The ordinary differential equation is transformed into a recurrence relation in one variable using the differential transformation. Approximate solution has the form of a Taylor polynomial whose coefficients are determined by solving the recurrence relation. Practical implementation of the presented algorithm is demonstrated in an example of the initial value problem for a differential equation with nonlinear nonconstant delay. A two-dimensional neutral system of higher complexity with constant, nonconstant, and proportional delays has been chosen to show numerical performance of the algorithm. Results are compared against Matlab function DDENSD.

Název v anglickém jazyce

Differential transform algorithm for functional differential equations with time-dependent delays

Popis výsledku anglicky

An algorithm using the differential transformation which is convenient for finding numerical solutions to initial value problems for functional differential equations is proposed in this paper. We focus on retarded equations with delays which in general are functions of the independent variable. The delayed differential equation is turned into an ordinary differential equation using the method of steps. The ordinary differential equation is transformed into a recurrence relation in one variable using the differential transformation. Approximate solution has the form of a Taylor polynomial whose coefficients are determined by solving the recurrence relation. Practical implementation of the presented algorithm is demonstrated in an example of the initial value problem for a differential equation with nonlinear nonconstant delay. A two-dimensional neutral system of higher complexity with constant, nonconstant, and proportional delays has been chosen to show numerical performance of the algorithm. Results are compared against Matlab function DDENSD.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

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

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

COMPLEXITY

ISSN

1076-2787

e-ISSN

—

Svazek periodika

2020

Číslo periodika v rámci svazku

Neuveden

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

12

Strana od-do

1-12

Kód UT WoS článku

000522423600004

EID výsledku v databázi Scopus

2-s2.0-85081256974