Solving Analytic Differential Equations in Polynomial Time over Unbounded Domains

  • Olivier Bournez
  • Daniel S. Graça
  • Amaury Pouly
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6907)


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.


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Copyright information

© Springer-Verlag GmbH Berlin Heidelberg 2011

Authors and Affiliations

  • Olivier Bournez
    • 1
  • Daniel S. Graça
    • 2
    • 3
  • Amaury Pouly
    • 4
  1. 1.Ecole Polytechnique, LIXPalaiseau CedexFrance
  2. 2.CEDMES/FCTUniversidade do Algarve, C. GambelasFaroPortugal
  3. 3.SQIG /Instituto de TelecomunicaçõesLisbonPortugal
  4. 4.Ecole Normale Supérieure de LyonFrance

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