Solving analytic differential equations in polynomial time over unbounded domains

Authors:
Olivier Bournez;Daniel S. Graça;Amaury Pouly
Affiliations:
Ecole Polytechnique, LIX, Palaiseau Cedex, France;FCT, Universidade do Algarve, Faro and SQIG, Instituto de Telecomunicações, Lisbon, Portugal;Ecole Normale Supérieure de Lyon, France
Venue:
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Year:
2011

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Abstract

In this paper we consider the computational complexity of solving initial-value problems defined with analytic ordinary differential equations (ODEs) over unbounded domains of Rn and Cn, 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.