Mixed Type Functional Differential Equations: Insight, Issues and
Applications
The seminar will focus on mixed-type functional dierential
equations (MTFDEs) of the form . The emphasis of our work (to date) with MTFDEs (also
referred to as forward-backward equations) has been on the
development of numerical approaches to the solution of this type of
equation. Alongside our continuing interest in this area we are now
seeking to apply our approach in modelling applications. These
equations are known to have application in nerve conduction theory,
one of our current areas of investigation. Parameter estimation is
a technique of interest to mathematical modellers. If the equation
being used by the modeller admits small solutions (solutions that
approach zero faster than any exponential) then no information is
obtained about the parameters. We have successfully detected the
presence of small solutions to several classes of delay dierential
equations (DDEs) using a numerical approach. We discuss the
potential for our work with DDEs to provide insight into the
detection of small solutions to MTFDEs and present illustrative
examples.
