Publication detail

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

REBENDA, J. PÁTÍKOVÁ, Z.

Original Title

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

English Title

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

Type

journal article in Web of Science

Language

en

Original Abstract

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.

English abstract

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.

Keywords

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

Released

28.02.2020

Publisher

Hindawi

Location

London, United Kingdom

Pages from

1

Pages to

12

Pages count

12

URL

Full text in the Digital Library

Documents

BibTex

``````
@article{BUT163422,
author="Josef {Rebenda} and Zuzana {Pátíková}",
title="Differential Transform Algorithm for Functional Differential Equations with Time-Dependent Delays",
annote="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.",