Abstract : In this paper we consider the computational complexity of solving initial-value problems defined with analytic ordinary differential equations (ODEs) over unbounded domains in $\R^n$ and $\C^n$. 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 over a strip on the complex plane.
https://hal-polytechnique.archives-ouvertes.fr/hal-00760919
Contributor : Olivier Bournez
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Submitted on : Tuesday, December 4, 2012 - 3:31:10 PM
Last modification on : Sunday, August 25, 2019 - 10:44:01 AM
Long-term archiving on : Tuesday, March 5, 2013 - 3:52:55 AM
