Computability of Ordinary Differential Equations

Abstract

In this paper we provide a brief review of several results about the computability of initial-value problems (IVPs) defined with ordinary differential equations (ODEs). We will consider a variety of settings and analyze how the computability of the IVP will be affected. Computational complexity results will also be presented, as well as computable versions of some classical theorems about the asymptotic behavior of ODEs.