Detail publikačního výsledku

Differential Transform Algorithm for Functional Differential Equations with Time-Dependent Delays

REBENDA, J.; PÁTÍKOVÁ, Z.

Originální název

Differential Transform Algorithm for Functional Differential Equations with Time-Dependent Delays

Anglický název

Differential Transform Algorithm for Functional Differential Equations with Time-Dependent Delays

Druh

Článek WoS

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.

Anglický 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

Klíčová slova v angličtině

Differential transformation; Functional differential equation; Time-dependent delay; Non-constant delay; Approximate solutions; Numerical comparison to Matlab

Autoři

REBENDA, J.; PÁTÍKOVÁ, Z.

Rok RIV

2021

Vydáno

28.02.2020

Nakladatel

Hindawi

Místo

London, United Kingdom

ISSN

1076-2787

Periodikum

COMPLEXITY

Svazek

2020

Číslo

1

Stát

Spojené státy americké

Strany od

1

Strany do

12

Strany počet

12

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

Complexity_Rebenda_Patikova_2020_2854574
2854574.f1