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Rigorous Numerical Computation of Polynomial Differential Equations Over Unbounded Domains

  • Olivier Bournez
  • Daniel S. GraçaEmail author
  • Amaury Pouly
Conference paper
  • 504 Downloads
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.

Keywords

Polynomial Ordinary Differential Equations Rigorous Numerical Calculations Unbounded Domains Maximum Allowable Error Theoretical Computer Science Literature 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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
    Email author
  • 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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