Research in computationally-based mathematics is a strong feature of the Department. There are active research programs in numerical analysis and scientific computing, together with links to other computational endeavours within the department and throughout the university. Both the MIR@W Program and the Applied and Computational Mathematics seminar provide a steady flow of visitors, whose interests lie in computational mathematics, to the department.

Dwight Barkley's work in computation centres on two areas. The first is the development of models and methods for fast, interactive simulations of reaction-diffusion partial-differential equations; he has developed and maintains codes released under the GNU public software license. The second area involves exploiting methods for large sparse linear systems to compute solutions and bifurcations in discretisations of partial-differential equations involving large numbers of variables.

Petr Plechac's research interests originate in numerical approximation of solutions to non-linear PDEs and from mathematical analysis of variational problems motivated by models in materials science and solid-state physics. His recent research work has focused on numerical analysis of methods for solving problems that exhibit multiple scales and development of efficient minimization strategies for non-convex variational problems. He also works in the analysis and implementation of adaptive methods and their application to approximation of singular solutions. He has been actively involved in several projects on design and implementation on different computer architectures of efficient parallel algorithms for solution of large systems of equations.

Andrew Stuart works primarily in the analysis and design of algorithms for dynamical systems and stochastic processes. His current research program is focussed on: (i) the approximation of stochastic differential equations, in particular regarding large-time behaviour; (ii) construction of coarse-grained stochastic models for large deterministic systems with random initial data; (iii) the study of coupled particle-field problems.

Other computationally-based research within the department includes work on Computational Group Theory and a variety of problems in applied mathematics where intensive simulation is central, such as Mathematical Biology. Interactions outside the department include the Centre for Scientific Computing, the Development and Theory of Algorithms and the High Performance Systems Group within Computer Science and a variety of problems in Scientific Computing, such as Computational Fluid Dynamics (Peter Carpenter, Eng and Mike Rudgyard, Comp. Sci).