In this paper we formulate a numerical structural stability result for delay equations with small delay under Euler discretization. The main ingredients of our approach are the existence and smoothness of small delay inertial manifolds, the C1-closeness of the small delay inertial manifolds and their numerical approximation and M.-C. Li's recent result on numerical structural stability of ordinary differential equations under the Euler method.
Bibliographical noteFunding Information:
Supported by DAAD project 323-PPP, Qualitative Theory of Numerical Methods for Evolution Equations in Infinite Dimensions. This work was done while the author was a visitor at the University of Bielefeld. The author would like to thank Prof. W.-J. Beyn for the stimulating discussions. The author is also grateful to the referee for his/her valuable comments.
- C -estimates
- Delay equations
- Euler method
- Numerical structural stability
- Small delay inertial manifolds