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Research

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Current research topics include:

Asymptotic and Perturbation Analysis

• Hyperasymptotics

Classical Analysis

• Axiomatic set theory
• Integro-differential equations
• Matrix inverse eigenvalue problems
• Singular parabolic partial differential equations

Computational Biology

• Biological control of insects
• Stochastic modelling of predator-prey systems
• Ultrasonically induced lung damage

Dynamical Systems

Engineering Mathematics

Geophysical Fluid Dynamics

• Multiscale theory and simulation
• Nonlinear tidal flow models
• Nonlinear waves
• Wave-mean flow interactions and associated instabilities

High Temperature Physics

• High temperature processing

Mathematics Education

• Educational role of technology including graphical calculators
• Effective use of computer algebra systems
• Student assessment and training using technology

Nonlinear Instability Theory

Numerical Analysis and Scientific Computing

Theoretical and computational fluid dynamics

• Moving boundary flow problems
• Simulation of free surface flows
• Vortex dynamics