Approximation of solutions of initial value problems for delay equations

Summary

In physics and nature, events usually cause effects that are delayed in time. For this reason, delay equations are increasingly used in applications to several fields, including engineering and biology. They give rise to dynamical systems in infinite-dimensional function spaces, so reliable approximations are necessary to enable the numerical analysis of the systems. This project will consider a particular approximation via pseudo-spectral methods and focus on the study of the convergence of the solutions of the initial value problems using tools from functional and complex analysis. Having a reliable numerical approximation at hand, this will be used to apply classical methods for model fitting and parameter estimation and investigate their performance when applied to delay equations.

The project would be carried on in collaboration with Professor Rossana Vermiglio, University of Udine, Italy

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