Will Wright

Post Doctoral Fellow

Department of Mathematical and Statistical Sciences
La Trobe University
Melbourne
Victoria 3086
Australia
Tel: +61 3 9479 2607
Fax: +61 3 9479 2466
Email: w.wright@latrobe.edu.au

M.Sc. 1999, Ph.D. 2003, Department of Mathematics, The University of Auckland, Auckland, New Zealand

Collaborators

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.

Publications

Preprints

J. C. Butcher, Z. Jackiewicz and W. M. Wright: Error propagation of general linear methods for ordinary differential equations, Submitted to J. Complexity.
H. Z. Munthe-Kaas and W. M. Wright: On the Hopf algebraic structure of Lie group integrators, Accepted in Found. Comput. Math..
H. Berland, B. Skaflestad and W. M. Wright: Expint — A Matlab package for exponential integrators, Accepted in ACM Trans. Math. Software.

Published

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.
J. C. Butcher and W. M. Wright: A transformation relating explicit and diagonally implicit general linear methods, Appl. Numer. Math., 44 (2003), 313-327.
W. M. Wright: Explicit general linear methods with inherent Runge-Kutta stability, Numer. Algorithms, 31 (2002), 381-399.
W. M. Wright: The construction of order 4 DIMSIMs for ordinary differential equations, Numer. Algorithms, 26 (2001), 123-130.

Theses

General linear methods with inherent Runge-Kutta stability, Ph.D. thesis, The University of Auckland, 2003.
General linear methods for ordinary differential equations, M.Sc. thesis, The University of Auckland, 1999.

Talks

The scaling and squaring technique for matrices related to the exponential, Conference on Geometric Integration, 18-22 September 2006, Castellon Spain.
Towards practical general linear methods, Innovative Integrators, 10-15 September 2006, Innsbruck Austria.
More on generalised Lawson methods, SciCADE, 10-15 May 2005, Nagoya Japan.
Exponential integrators: A review, ANZIAM, 30 January - 4 February 2005, Napier New Zealand.

Upcoming conferences

Conference on Geometric Integration 18-22 September, 2006, Castellon, Spain.
Innovative Integrators for Differential and Delay Equations 10-15 September, 2006, Innsbruck, Austria.
11th Seminar NUMDIFF, 4-8 September 2006, Halle, Germany.