Equacions diferencials ordinàries i diferenciació automàtica

Abstract

[en] Automatic differentiation is an alternative method to compute the derivatives of a function in a given point. This method requires that the function can be written as a sequence of elementary operations and basic functions like exponential or trigonometry ones. Once we have our function as a combination of those elements, we can compute it and find its derivatives. Moreover, there are the Poincaré sections. This is a really common tool used to study dynamical systems, but the computation of its derivatives used to be a frequent computational problem. In order to solve this, we can use automatic differentiation. More precisely, we will study how to modify a numerical integrator to compute automatically the derivatives of the flow of a differential equation regarding some initial conditions. The numerical integrator that we will use is Runge-Kutta-Fehlberg of order 4 and 5.