Mathematics Colloquium 04/28/23

Abstract:  Runge--Kutta methods, discovered about 130 years ago, are used to find numerical approximations to the solution of initial-value problems.  In the computer age they have become sophisticated enough to faithfully simulate complex physical systems through extended time periods.  The study of the numerical properties of these schemes makes use of algebraic structures related to rooted trees.  In this colloquium, several of these topics will be touched on, with the history of increasingly complicated Runge--Kutta methods serving as a unifying theme.

Biosketch: Professor Butcher is recognized as the founder of the modern theory of Runge-Kutta methods, one of the principal classes of numerical methods for solving ordinary differential equations. The Butcher group, Butcher tableau, Butcher series in Numerical Analysis and the Butcher prize are named after him. He was a fellow of SIAM and FRSNZ (the Royal Society of New Zealand). He has received many awards and honors, including the Hector Medal (1996), the Research Award and Jones Medal from the Royal Society of New Zealand and New Zealand Mathematical Society in 2010 for his "exceptional lifetime work on numerical methods for the solution of differential equations and leadership in the development of New Zealand mathematical sciences.", and the Van Wijngaarden Prize from Netherland in 2011. In the 2013 Queen's Birthday Honours, he was appointed an Officer of the New Zealand Order of Merit, for services to mathematics.

Professor Butcher had supervised many PhD students, many of whom hold prestigious positions worldwide. He was a founding member and the former president of the New Zealand Mathematical Society, and the former Head of Department of Mathematics, the University of Auckland, New Zealand. In 2021, at the age of 88, he published his popular book on “B-Series: Algebraic Analysis of Numerical Methods”.

For more information, please contact:  Dr. Vu Thai Luan (luan@math.msstate.edu).