Nic Fillion (SFU) will join us online on Friday March 28th, 15:30 CET for a talk on how perturbation theory (perhaps) differs between physics and numerical mathematics. You can join using the following webex link: https://unistuttgart.webex.com/meet/nico.formanek
Abstract:
Although perturbation methods are very widespread, being used to find approximate solutions to all kinds of mathematical problems, there are profound discrepancies between how different people think about them. This paper will elaborate on differences between the mathematicians’ and the physicists’ way of thinking about perturbation methods, and I will use the WKB method as my running example. After a brief historical discussion of the method, I will suggest that what distinguishes the two modes of thinking is not only that one is more mathematically rigorous whereas the other rests on physical intuitions, but rather that they embody different perspectives on approximation. I will show how a simple error-theoretic framework common among numerical analysts–backward-error analysis–can beneficially be applied to the assessment of perturbative solutions.