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

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dc.contributor.authorRebenda, Josefcs
dc.contributor.authorPátíková, Zuzanacs
dc.coverage.issue1cs
dc.coverage.volume2020cs
dc.date.accessioned2020-08-04T11:00:28Z
dc.date.available2020-08-04T11:00:28Z
dc.date.issued2020-02-28cs
dc.description.abstractAn 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.en
dc.formattextcs
dc.format.extent1-12cs
dc.format.mimetypeapplication/pdfcs
dc.identifier.citationCOMPLEXITY. 2020, vol. 2020, issue 1, p. 1-12.en
dc.identifier.doi10.1155/2020/2854574cs
dc.identifier.issn1076-2787cs
dc.identifier.other163422cs
dc.identifier.urihttp://hdl.handle.net/11012/186778
dc.language.isoencs
dc.publisherHindawics
dc.relation.ispartofCOMPLEXITYcs
dc.relation.urihttps://www.hindawi.com/journals/complexity/2020/2854574/cs
dc.rightsCreative Commons Attribution 4.0 Internationalcs
dc.rights.accessopenAccesscs
dc.rights.sherpahttp://www.sherpa.ac.uk/romeo/issn/1076-2787/cs
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/cs
dc.subjectDifferential transformationen
dc.subjectFunctional differential equationen
dc.subjectTime-dependent delayen
dc.subjectNon-constant delayen
dc.subjectApproximate solutionsen
dc.subjectNumerical comparison to Matlaben
dc.titleDifferential Transform Algorithm for Functional Differential Equations with Time-Dependent Delaysen
dc.type.driverarticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen
sync.item.dbidVAV-163422en
sync.item.dbtypeVAVen
sync.item.insts2020.08.04 13:00:28en
sync.item.modts2020.08.04 12:17:15en
thesis.grantorVysoké učení technické v Brně. Středoevropský technologický institut VUT. Kybernetika pro materiálové vědycs
thesis.grantorVysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií. Ústav matematikycs
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Kybernetika pro materiálové vědy