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Travelling Waves and Function Differential Equations with Advances and Delays
Mixed Type Functional Differential Equations with Advances and Delays arise in a surprisingly wide range of applications, from physics to biology to control systems, most recently receiving significant attention because travelling wave solutions to lattice differential equations are defined by FDE boundary value problems on an unbounded domain. The presence of advances as well as delays results in FDE initial value problems not being well-posed in general. Analytical study of such problems would be greatly aided by the existence of good numerical solutions. We show how to compute numerical solutions using a collocation boundary value problem method, paying attention to the modelling of the tails after truncation to a finite computational interval. Travelling wave solutions of a spatially discrete Nagumo equation illustrate the issues that arise.
Date: 2004-09-10 à 05:30
Endroit: Local 2744, pavillon Adrien-Pouliot