On approximation of the solutions of delay differential equations by using piecewise constant arguments

On approximation of the solutions of delay differential equations by using piecewise constant arguments

By using the Gronwall Bellman inequality we prove some limit relations between the solutions of delay differential equations with continuous arguments and the solutions of some related delay differential equations with piecewise constant arguments(EPCA). EPCA are strongly related to some discrete di...

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Bibliographic Details
Main Author: Istevan Györi
Format: Article
Language:English
Published: Hindawi Limited 1991-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
differential equations of retarded and neutral types
differential equations with piecewise constant arguments
numerical approximation of solutions
difference equations.
Online Access:http://dx.doi.org/10.1155/S016117129100011X
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spelling doaj-b569eeb20d8a4d34910616fc03939e7a2020-11-24T22:48:54ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251991-01-0114111112610.1155/S016117129100011XOn approximation of the solutions of delay differential equations by using piecewise constant argumentsIstevan Györi0Department of Mathematics, The University of Rhode Island, Kingston 02881, Rhode Island, USABy using the Gronwall Bellman inequality we prove some limit relations between the solutions of delay differential equations with continuous arguments and the solutions of some related delay differential equations with piecewise constant arguments(EPCA). EPCA are strongly related to some discrete difference equations arising in numerical analysis, therefore the results can be used to compute numerical solutions of delay differential equations. We also consider the delay differential equations of neutral type by applying a generalization of the Gronwall Bellman inequality.http://dx.doi.org/10.1155/S016117129100011Xdifferential equations of retarded and neutral types differential equations with piecewise constant argumentsnumerical approximation of solutionsdifference equations.
collection DOAJ
language English
format Article
sources DOAJ
author Istevan Györi
spellingShingle Istevan Györi
On approximation of the solutions of delay differential equations by using piecewise constant arguments
International Journal of Mathematics and Mathematical Sciences
differential equations of retarded and neutral types
differential equations with piecewise constant arguments
numerical approximation of solutions
difference equations.
author_facet Istevan Györi
author_sort Istevan Györi
title On approximation of the solutions of delay differential equations by using piecewise constant arguments
title_short On approximation of the solutions of delay differential equations by using piecewise constant arguments
title_full On approximation of the solutions of delay differential equations by using piecewise constant arguments
title_fullStr On approximation of the solutions of delay differential equations by using piecewise constant arguments
title_full_unstemmed On approximation of the solutions of delay differential equations by using piecewise constant arguments
title_sort on approximation of the solutions of delay differential equations by using piecewise constant arguments
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 1991-01-01
description By using the Gronwall Bellman inequality we prove some limit relations between the solutions of delay differential equations with continuous arguments and the solutions of some related delay differential equations with piecewise constant arguments(EPCA). EPCA are strongly related to some discrete difference equations arising in numerical analysis, therefore the results can be used to compute numerical solutions of delay differential equations. We also consider the delay differential equations of neutral type by applying a generalization of the Gronwall Bellman inequality.
topic differential equations of retarded and neutral types
differential equations with piecewise constant arguments
numerical approximation of solutions
difference equations.
url http://dx.doi.org/10.1155/S016117129100011X
work_keys_str_mv AT istevangyori onapproximationofthesolutionsofdelaydifferentialequationsbyusingpiecewiseconstantarguments
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