Solving Analytic Differential Equations in Polynomial Time over Unbounded Domains

In this paper we consider the computational complexity of solving initial-value problems defined with analytic ordinary differential equations (ODEs) over unbounded domains of R and C, under the Computable Analysis setting. We show that the solution can be computed in polynomial time over its maximal interval of definition, provided it satisfies a very generous bound on its growth, and that the function admits an analytic extension to the complex plane.