# 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} }

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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