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Rigorous Numerical Computation of Polynomial Differential Equations Over Unbounded Domains

  • Olivier Bournez
  • Daniel S. Graça
  • Amaury Pouly
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9582)

Abstract

In this abstract we present a rigorous numerical algorithm which solves initial-value problems (IVPs) defined with polynomial differential equations (i.e. IVPs of the type \(y'=p(t,y)\), \(y(t_0)=y_0\), where p is a vector of polynomials) for any value of t. The inputs of the algorithm are the data defining the initial-value problem, the time T at which we want to compute the solution of the IVP, and the maximum allowable error \(\varepsilon >0\). Using these inputs, the algorithm will output a value \(\tilde{y}_T\) such that \(\Vert \tilde{y}_T-y(T)\Vert \le \varepsilon \) in time polynomial in T, \(-\log \varepsilon \), and in several quantities related to the polynomial IVP.

Notes

Acknowledgments

D. Graça was partially supported by Fundação para a Ciência e a Tecnologia and EU FEDER POCTI/POCI via SQIG - Instituto de Telecomunicações through the FCT project UID/EEA/50008/2013.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Olivier Bournez
    • 1
  • Daniel S. Graça
    • 2
    • 3
  • Amaury Pouly
    • 1
    • 2
  1. 1.LIXEcole PolytechniquePalaiseau CedexFrance
  2. 2.CEDMES/FCTUniversidade do AlgarveFaroPortugal
  3. 3.SQIG/Instituto de TelecomunicaçõesLisbonPortugal

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