Staff profile

Qualifications

• M.Sc. 1999, Ph.D. 2003 (University of Auckland).

Research interests

My research is concerned with the construction and analysis of algorithms for the numerical solution of ordinary and partial differential equations. In particular, my research is focussed on the following three areas:

 

• General linear methods a class of numerical integrators which encompass as special cases the linear multistep and Runge-Kutta methods. Schemes with a property known as inherent Runge-Kutta stability have been identified as likely candidates for inclusion in a robust code.
• Geometric integration is concerned with the construction of numerical algorithms which preserve some of the dynamical properties of the exact solution. B-series and Hopf algebras provide a pruely algebraic way of classifying such methods.
• Exponential integrators in conjunction with spectral methods or finite difference approximations can lead to very efficient schemes for the numerical solution of semi-linear partial differential equations. Exponential integrators have close connections with geometric integrators and the most efficient schemes are likely to be generalisations of the general linear methods.

Recent publications and presentations

• A. Ostermann, M. Thalhammer and W. M. Wright: A class of explicit exponential general linear methods, BIT, 46 (2006), 409-431.
• J. C. Butcher and W. M. Wright: Applications of doubly companion matrices, Appl. Numer. Math., 56 (2006), 358-373.
• B. V. Minchev and W. M. Wright: A review of exponential integrators for first order semi-linear problems, Tech. Rep. NTNU, (2005), 1-44.
• J. C. Butcher and W. M. Wright: The construction of practical general linear methods, BIT, 43 (2003), 695-721.