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REBENDA, J. PÁTÍKOVÁ, Z.
Originální název
Differential Transform Algorithm for Functional Differential Equations with Time-Dependent Delays
Typ
článek v časopise ve Web of Science, Jimp
Jazyk
angličtina
Originální abstrakt
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.
Klíčová slova
Differential transformation; Functional differential equation; Time-dependent delay; Non-constant delay; Approximate solutions; Numerical comparison to Matlab
Autoři
REBENDA, J.; PÁTÍKOVÁ, Z.
Vydáno
28. 2. 2020
Nakladatel
Hindawi
Místo
London, United Kingdom
ISSN
1076-2787
Periodikum
COMPLEXITY
Ročník
2020
Číslo
1
Stát
Spojené státy americké
Strany od
Strany do
12
Strany počet
URL
https://www.hindawi.com/journals/complexity/2020/2854574/
Plný text v Digitální knihovně
http://hdl.handle.net/11012/186778
BibTex
@article{BUT163422, author="Josef {Rebenda} and Zuzana {Pátíková}", title="Differential Transform Algorithm for Functional Differential Equations with Time-Dependent Delays", journal="COMPLEXITY", year="2020", volume="2020", number="1", pages="1--12", doi="10.1155/2020/2854574", issn="1076-2787", url="https://www.hindawi.com/journals/complexity/2020/2854574/" }
Dokumenty
2854574.f1.txt Complexity_Rebenda_Patikova_2020_2854574.pdf