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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1991-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S016117129100011X |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832567612212510720 |
|---|---|
| author | Istevan Györi |
| author_facet | Istevan Györi |
| author_sort | Istevan Györi |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-b569eeb20d8a4d34910616fc03939e7a |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1991-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-b569eeb20d8a4d34910616fc03939e7a2025-02-03T01:01:01ZengWileyInternational 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. |
| 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. |
| title | 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_short | 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 |
| 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 |