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My research on dynamical systems has included work on vibro-impacting systems, population dynamics, nonlinear phenomena in power networks and economic modelling. The common theme in all of the above is the presence of discontinuities in the mathematical models.
My work in numerical analysis has been the analysis and development of adaptive timestepping algorithms for both Ordinary and Stochastic Differential Equations.
Recent work in the area of economics has focused on the development and analysis of models that mimic the ways in which human psychology affects the dynamics of financial markets.
You can download my recent preprints in PDF format below. Click here for links to, or copies of, my publications.
An adaptive Euler-Maruyama scheme for SDEs: Convergence and stability (with Jonathan Mattingly and Andrew Stuart) PDF file
The effective stability of adaptive timestepping ODE solvers (to appear SIAM J. Num. Anal.) PDF file
Mean-square stability of an adaptive SDE solver (with Tim Seaman, to appear J. Comp. App. Math.) PDF file
Market statistics of a psychology-based heterogeneous agent model (with Tim Seaman, to appear Int. J. Theor. Appl. Fin.) PDF file
A mean-field model of investor behaviour (with Rod Cross and Michael Grinfeld ) PDF file
Stylized facts from a threshold-based heterogeneous agent model (with Rod Cross, Michael Grinfeld and Tim Seaman ) PDF file
Stepsize control for the Milstein scheme using first-exit-times PDF file
Rational Expectations, psychology and inductive learning via moving thresholds (with Tim Seaman) PDF file
Hysteresis and Economics (with Rod Cross and Michael Grinfeld ) PDF file
Centre for Mathematical Sciences, University of Cambridge, UK (Undergraduate and Part III)
Department of Mathematics, University of
Bristol, UK (PhD)
Department of Mathematics, University of Strathclyde, UK (Post-doctoral position)
Scientific Computing and Computational Mathematics Program, Stanford University, USA (Post-doctoral position)