In this paper we consider the computational complexity of solving initial-value problems defined with analytic ordinary differential equations (ODEs) over unbounded domains of ℝn and ℂn, under the Computable Analysis setting. We show that the solution can be computed in polynomial time over its maximal interval of definition, provided it satisfies a very generous bound on its growth, and that the function admits an analytic extension to the complex plane. © 2011 Springer-Verlag GmbH.
CITATION STYLE
Bournez, O., Graça, D. S., & Pouly, A. (2011). Solving analytic differential equations in polynomial time over unbounded domains. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6907 LNCS, pp. 170–181). https://doi.org/10.1007/978-3-642-22993-0_18
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