The HADES seminar on Tuesday, October 29th, will be at 2:00pm in Room 740.

Speaker: James Rowan

Abstract: Computers cannot do exact arithmetic with arbitrary real numbers. But as analysts, that shouldn’t bother us too much since we usually deal in inequalities; often, we only need upper and lower bounds. I will give an introduction to interval arithmetic and survey some ways to make rigorous use of numerics in PDE proofs. First, I will discuss an interval arithmetic version of Newton’s method for root-finding and illustrate its use to compute a threshold value of a physical parameter in a solitary water waves problem (from joint work with Lizhe Wan). Then I will discuss the use of interval arithmetic to “upgrade” approximate solutions to nearby exact solutions and give a survey of some recent developments in this area that have inspired some recent projects I have been working on.