| Speaker: Emeritus Professor John Butcher Affiliation: The University of Auckland Time: 2 pm Thursday, 16 August, 2018 Location: 303S-561 |
| The graphs, known as trees, have applications in many parts of mathematics and science, such as non-commutative geometry, quantum field theory, stochastic processes and numerical methods for ordinary differential equations. The applications discussed in this seminar are the accuracy and the conservation of invariants, for so-called B-series methods, including Runge-Kutta methods. Related graphical structures, such as forests, stumps and free trees also play a role alongside trees. The composition group for B-series enables new questions to be asked, such as conjugate order of numerical methods. The early studies of Runge and Kutta, and others, defined order of accuracy in terms of a generic scalar test problem. It is now known that the conclusions from this classical theory are not generally applicable to high dimensional problems. This will be illustrated by the derivation of a method with ambiguous order. |