Catherine Drysdal, University of Birmingham
In this talk, I look at two examples regarding the numerical computation of spectra for infinite-dimensional non-self-adjoint operators. Two conditions are need to compute the spectrum of operators in one limit. Namely, knowledge of how the operator acts on vectors and also how the resolvent norm behaves near the spectrum. We will explore two examples that illustrate the two conditions and how we can overcome them in certain context. Regarding the first condition, we explore an explosive-convection diffusion equation and regarding the second we explore a non-self-adjoint Ginzburg-Landau equation, where we have a quasi-basis structure.
