Dynamics seminar by Jason Mireles James (Florida Atlantic University) on 28 February

On Wednesday 28th of February at 4pm in the MathLab, Jason Mireles James (Florida Atlantic University) will give an Amsterdam Dynamics seminar.

The talk will take place in the Maryam seminar room (9A-46) and everyone is welcome to join for drinks at Bar Boele after the talk.

Title: Power series manipulation with the FFT: examples and error bounds

Abstract: state-of-the-are computational methods for computing invariant manifolds often require manipulation of high order power series expansions.  For polynomial problems this can be done in a straightforward way using Cauchy products.  For non-polynomial problems with nonlinear terms involving elementary functions, it is possible to transform to a polynomial system by appending the differential equations solved by the elementary function.  Yet, for complicated enough expressions this becomes cumbersome, and for problems with implicitly defined nonlinearities, or nonlinearities involving compositions with the unknown function, it may be impractical or even impossible.  

An alternative is to use methods based on interpolation.  I'll talk about one possibility, which is to use the discrete Fourier transform.  If one is interested in computer assisted proofs, then it is important to bound all discretization/truncation errors, including the so called ailiasing error.  I'll review some classical error bounds and show how they can be used in the context of Newton-Kantorovich type arguments.