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Rigorous Numerical Computation of Polynomial Differential Equations Over Unbounded Domains

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 9582)


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.


  • Polynomial Ordinary Differential Equations
  • Rigorous Numerical Calculations
  • Unbounded Domains
  • Maximum Allowable Error
  • Theoretical Computer Science Literature

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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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Correspondence to Daniel S. Graça .

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Bournez, O., Graça, D.S., Pouly, A. (2016). Rigorous Numerical Computation of Polynomial Differential Equations Over Unbounded Domains. In: Kotsireas, I., Rump, S., Yap, C. (eds) Mathematical Aspects of Computer and Information Sciences. MACIS 2015. Lecture Notes in Computer Science(), vol 9582. Springer, Cham.

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  • Print ISBN: 978-3-319-32858-4

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