Numerical methods for differential equations as a mathematical science

Start: 04/21/2010 - 4:15pm
End  : 04/21/2010 - 5:15pm


John Butcher (University of Auckland, New Zealand)


Because of the practical needs of science and engineering, numerical methods can be looked at in purely utilitarian terms, as a minor adjunct to mathematical modeling. On the other hand, scientific calculations often make intense demands at the limit of computational capabilities, and hence fit into a computer science setting. But numerical analysis is also a significant mathematical science, using tools from other parts of mathematics and even contributing to them.

For many computational questions the paradigm of using only what is required, that is only using elementary mathematics whenever this is possible, is the right approach. But in the study of numerical methods for initial value problems, there are good reason for going outside this paradigm. Starting from the question of analysing the accuracy of Runge-Kutta methods, this seminar will show how questions involving graph theory and combinatorics have a natural role and this leads onto more abstract algebraic structures as more elaborate numerical schemes are investigated.

Beckman B126, Harvey Mudd College

Misc. Information

Coffee & Cookies will be served at 3:45 pm in Olin B161 Harvey Mudd College.

The speaker will give this talk electronically via Skype from New Zealand. The talk will be hosted and arbitrated by Lenny Fukshansky. This is our first experiment with electronic talks that are becoming more popular. There will be no dinner for this talk.