On the complexity of solving initial value problems

@article{Bournez2012OnTC,
  title={On the complexity of solving initial value problems},
  author={O. Bournez and D. Graça and A. Pouly},
  journal={ArXiv},
  year={2012},
  volume={abs/1202.4407}
}
  • O. Bournez, D. Graça, A. Pouly
  • Published 2012
  • Computer Science, Mathematics
  • ArXiv
  • In this paper we prove that computing the solution of an initial-value problem y = <i>p</i>(<i>y</i>) with initial condition <i>y</i>(<i>t</i><sub>0</sub>) = <i>y</i><sub>0</sub> ∈ R<sup><i>d</i></sup> at time <i>t</i><sub>0</sub> + <i>T</i> with precision 2<sup>−μ</sup> where <i>p</i> is a vector of polynomials can be done in time polynomial in the value of <i>T</i>, μ and <i>Y</i> = [equation]. Contrary to existing results, our algorithm works over any bounded or unbounded domain. Furthermore… CONTINUE READING

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