### Abstract

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.

Original language | English |
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Pages (from-to) | 111-126 |

Number of pages | 16 |

Journal | International Journal of Mathematics and Mathematical Sciences |

Volume | 14 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1991 |

### Fingerprint

### Keywords

- difference equations
- Differential equations of retarded and neutral types
- differential equations with piecewise constant arguments
- numerical approximation of solutions

### ASJC Scopus subject areas

- Mathematics (miscellaneous)

### Cite this

**On Approximation of the Solutions of Delay Differential Equations By Using Piecewise Constant Arguments.** / Győri, I.; Györi, Istvan.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - On Approximation of the Solutions of Delay Differential Equations By Using Piecewise Constant Arguments

AU - Győri, I.

AU - Györi, Istvan

PY - 1991

Y1 - 1991

N2 - 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.

AB - 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.

KW - difference equations

KW - Differential equations of retarded and neutral types

KW - differential equations with piecewise constant arguments

KW - numerical approximation of solutions

UR - http://www.scopus.com/inward/record.url?scp=0001506014&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001506014&partnerID=8YFLogxK

U2 - 10.1155/S016117129100011X

DO - 10.1155/S016117129100011X

M3 - Article

AN - SCOPUS:0001506014

VL - 14

SP - 111

EP - 126

JO - International Journal of Mathematics and Mathematical Sciences

JF - International Journal of Mathematics and Mathematical Sciences

SN - 0161-1712

IS - 1

ER -