Shannon's general purpose analog computer (GPAC) is an elegant model of analog computation in continuous time. In this paper, we consider whether the set G of GPAC-computable functions is closed under iteration, that is, whether for any function f(x)∈G there is a function F(x, t)∈G such that F(x, t)=f^t(x) for nonnegative integers t. We show that G is not closed under iteration, but a simple extension of it is. In particular, if we relax the definition of the GPAC slightly to include unique solutions to boundary value problems, or equivalently if we allow functions x^kθ(x) that sense inequalities in a differentiable way, the resulting class, which we call G +θ_k, is closed under iteration. Furthermore, G +θ_k includes all primitive recursive functions and has the additional closure property that if T(x) is in G +θ_k, then any function ofx computable by a Turing machine in T(x) time is also.