Abstract We consider an adaptive interpolation algorithm for numerical integration of systems of ordinary differential equations (ODEs) with interval parameters and initial conditions. At each time moment, a piecewise polynomial function of a prescribed degree is constructed in the course of algorithm operation that interpolates the dependence of the solution on particular values of interval uncertainties with a controlled accuracy. We study the question of computational costs of the algorithm. An analytic estimate is derived for the number of operations; it depends on the algorithm parameters, in particular, the degree of interpolation and the specific features of the ODE system being integrated. Using a number of representative examples of various dimension and containing a varying number of interval uncertainties, we show that there exists an optimum value of interpolation degree from the viewpoint of computational costs.

中文翻译：

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带区间参数常微分方程组数值解的一种自适应插值算法的分析与优化

摘要 我们考虑了一种自适应插值算法，用于对具有区间参数和初始条件的常微分方程 (ODE) 系统进行数值积分。在每个时刻，在算法操作过程中构建规定次数的分段多项式函数，该函数以受控精度内插解对区间不确定性的特定值的依赖性。我们研究算法的计算成本问题。对操作次数进行分析估计；它取决于算法参数，特别是插值的程度和被集成的 ODE 系统的具体特征。使用多个具有不同维度并包含不同数量区间不确定性的代表性示例，