# Matthew King

###### Current Work:

I have just entered my second year of MASDOC, beginning the PhD under the supervision of Dr. E. Brambley. My current work is a continuation of my MASDOC masters thesis and has applications in aeroacoustics. It focuses on the behaviour of an invisid compressible fluid flow through a 3D cylindrical duct. In particular I am considering a flow that is uniform away from the boundary, and has a sheared profile within the resulting boundary layer.

###### Background:

During the first year of MASDOC as a part of the course I have worked alongside three of my colleagues on a group research project on the topic of Summation by Parts. This is a finite difference scheme for the numerical approximation of derivatives. In this project we looked at two different approaches for construction of these schemes; a brute force linear algebra method, and an approach making use of interpolating basis functions. The latter did not have much literature and we made clear sufficient conditions for attainment of specific degrees of accuracy among other result.

Prior to coming to Warwick I have studied an MMath degree at the University of Sussex. Here I focused on the analysis of Differential Equations and completed a masters project under the title ‘Analysis of Delay Differential Equations and their Application in Population Dynamics.’ This was supervised by Dr Yuliya Kyrychko. This looked at some of the basics behind steady state behaviour of delay differential equations with constant time delays, $\frac{dX}{dt}(t)=X(t, t-\tau)$. This was observed in the setting of population growth models, and then observed further application to models for the spread of the Zika Virus.