A note on continuous dependence of solutions of dynamic equations on time scales

Abstract

We give a precise formulation and a proof as constructive as possible of the widely accepted claim that solutions of a dynamic equation depend continuously on the base time scale. Our approach to this problem is via Euler polygons which opens possibilities for development of numerical analysis of dynamic equations on time scales.

Keywords:

• time scales
• dynamic equations
• continuous dependence
• Hausdorff metric

AMS Classifications::

• 34A05
• 34A30
• 35C99
• 39A99

Acknowledgements

The author is indebted to the anonymous referee for helpful comments and suggestions that greatly improved the paper. Research supported by the Czech Grant Agency under grant 201/08/0469.