Abstract
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 C 1-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.
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Farkas, G. Small Delay Inertial Manifolds Under Numerics: A Numerical Structural Stability Result. Journal of Dynamics and Differential Equations 14, 549–588 (2002). https://doi.org/10.1023/A:1016335115301
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DOI: https://doi.org/10.1023/A:1016335115301