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

• 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
• ISSN: 0161-1712; 1687-0425

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.