Current Research Sponsors

Engineering and Physical Sciences Research Council.

INTAS program of the European Union.

Wales Institute of Mathematical and Computational Sciences.

I am a member of the
Analysis and Differential Equations Group in Cardiff.

My interests are in spectral problems for ordinary and partial differential operators.

My most recent work has been on the numerical solution of spectral problems for ODEs and PDEs on infinite domains. Central to this has been the study of the Titchmarsh-Weyl function for the ODE case, and of the Dirichlet to Neumann map for the PDE case.

I also work on inverse problems in spectral theory: these involve determining a problem from a knowledge of its spectral properties, usually through the Dirichlet to Neumann map, and have numerous applications. See the article of Chu and Golub for a review.

I have been interested in mathematical software ever since NAG sponsored my PhD, and work on special numerical methods for eigenvalue problems. For ODE eigenvalue problems it is particularly important to use numerical methods which preserve as many qualitative features of the original equation as possible. The huge explosion of work on Geometric Integration, much of it based on the work of physicists dating back at least to the 1950s, has been vital for much of the recent software for eigenvalue problems.