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Solving Analytic Differential Equations in Polynomial Time over Unbounded Domains

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Mathematical Foundations of Computer Science 2011 (MFCS 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,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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Bournez, O., Graça, D.S., Pouly, A. (2011). Solving Analytic Differential Equations in Polynomial Time over Unbounded Domains. In: Murlak, F., Sankowski, P. (eds) Mathematical Foundations of Computer Science 2011. MFCS 2011. Lecture Notes in Computer Science, vol 6907. Springer, Berlin, Heidelberg.

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  • Print ISBN: 978-3-642-22992-3

  • Online ISBN: 978-3-642-22993-0

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