Archivio mensile:luglio 2016

Seminario di Roberto Castelli, 14 luglio 2016, ore 15:30

Si avvisa che Giovedì 14 luglio 2016, alle ore 15:30, in aula 3014, il dr. Roberto Castelli (VU University Amsterdam) terrà il seminario

 

“Rigorous computations to study nonlinear differential equations”

 

ABSTRACT

The motion of a fluid, the movements of celestial bodies, the suspension of a bridge, the pattern formation in chemical reactions are all examples of phenomena modelled by non linear differential equations. The presence of nonlinearities represents a severe complication in the study of these equations by analytical techniques. On the other side numerical simulations can face a larger spectra of problems, providing approximate solutions at the expenses of the mathematical rigorousness.

The primary goal of rigorous computations is to fill-in this gap: combining analytical theories and scientific computing, the aim is to prove theorems, in the rigorous mathematical sense, with the assistance of a computer. The existence of complicated dynamics, the multiplicity of solutions, the bifurcation diagram of steady states, existence of heteroclinic connections are some examples of solutions proven by means of rigorous numerics.

This talk is intended as an introduction of the field of rigorous computation. A method based on the contraction mapping theorem will be discussed in more details and some example of solutions for nonlinear differential problems (both ODEs and PDEs) will be presented.

 

Tutti gli interessati sono cordialmente invitati a partecipare.