Solving ODE eigenvalue problems with rigorous computation

Friday, December 2, 2022 - 11:00am for 1 hour (actually 50 minutes)
Blake Barker – Brigham Young University –
Jorge Gonzalez

Abstract: ODE eigenvalue problems often arise in the study of stability of traveling waves, in showing the second variation of a functional is positive definite, and in many other applications. For many eigenvalue problems, it is not possible to obtain an explicit eigen pair. Thus, one uses numerical methods to approximate the solution. By rigorously bounding all errors in the computation, including computer rounding errors via use of an interval arithmetic package, one may obtain a computer assisted proof that the true solution lies in a small neighborhood of an approximation. This allows one to prove stability of traveling waves, for example. In this talk, we discuss recent work regarding computer assisted proof of stability of waves, and discuss other areas of application, such as in identifying most probable paths of escape in stochastic systems.