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Analysis and Optimization of an Adaptive Interpolation Algorithm for the Numerical Solution of a System of Ordinary Differential Equations with Interval Parameters

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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.

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Authors and Affiliations

  1. Federal Research Center “Computer Science and Control,” Russian Academy of Sciences, Moscow, 119333, Russia

    A. Yu. Morozov, A. A. Zhuravlev & D. L. Reviznikov

  2. Moscow Aviation Institute, Moscow, 125993, Russia

    A. Yu. Morozov & D. L. Reviznikov

Authors
  1. A. Yu. Morozov
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  2. A. A. Zhuravlev
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  3. D. L. Reviznikov
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Correspondence to A. Yu. Morozov, A. A. Zhuravlev or D. L. Reviznikov.

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Translated by V. Potapchouck

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Morozov, A.Y., Zhuravlev, A.A. & Reviznikov, D.L. Analysis and Optimization of an Adaptive Interpolation Algorithm for the Numerical Solution of a System of Ordinary Differential Equations with Interval Parameters. Diff Equat 56, 935–949 (2020). https://doi.org/10.1134/S0012266120070125

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