Jason Mireles James

Florida Atlantic University, Department of Mathematical Sciences

Periodic solutions of differential equations: automatic differentiation for Fourier series and computer assisted proof

I will recall the basic idea of automatic differentiation for Taylor series solutions of initial value problems. Then we will look at how to adapt automatic differentiation to compute Fourier series expansions of periodic orbits. My main goal in this discussion is to obtain some computer assisted existence proofs based on these ideas, and give some applications.