My research interests are in the area of applied computational mathematics.
I am interested in developing efficient numerical techniques to simulate systems numerically on a computer and in proving convergence of these methods. Much of my recent work has looked at the role of noise in systems and how this can be simulated and methods for reducing uncertainty and hence obtain better predictions. I am interested in the efficient simulation of porous media flows - such as contamination of ground water or modelling of underground reservoirs, eg relevant to petroleum. These models are typically stochastic PDEs with advection diffusion and reaction terms. I also research in computational neuroscience looking at models at the single neuron scale - these might be a mix of stochastic PDEs and stochastic ODEs. I am also interested in models of neural fields- these are typically time dependent integral equations.