Solving Analytic Differential Equations in Polynomial Time over Unbounded Domains
Solving Analytic Differential Equations in Polynomial Time over Unbounded Domains
复制标题
求解无界域上多项式时间内的解析微分方程
DOI：
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发表时间：
2011
期刊：
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通讯作者：
Amaury Pouly
中科院分区：
文献类型：
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作者：
Olivier Bournez;D. Graça;Amaury Pouly
在本文中，我们考虑的计算复杂性的求解定义的解析常微分方程（ODE）在无界区域的Rn和Cn的初值问题，在可计算分析设置。我们证明，只要该解满足其增长的非常宽松的界限，并且该函数允许对复平面进行解析扩展，则可以在其最大定义区间内以多项式时间计算该解。
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.