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Abstract <p>Fundamentals of fast universal discrete orthogonal trigonometric interpolations for non-periodic functions are presented enabling highly accurate approximate solution of differential problems to be obtained. Using the method of fast universal discrete orthogonal trigonometric interpolations and extrapolations, an approximate analytical solution to the problem of finding the trajectory of a flying vehicle is obtained, and the coordinates of its rendezvous with another flying vehicle are determined. Numerical experiments showed that in the test problem under consideration where the flying vehicle trajectories are described by low-degree polynomials, the relative error in finding the coordinates does not exceed 0.1%, and the calculation time does not exceed 25 seconds.</p>

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Using Universal Fast Trigonometric Interpolation and Extrapolation to Determine the Coordinates of Rendezvous of Two Flying Vehicles in the Earth’s Atmosphere

  • 期刊论文

  • 发表日期：

    2026年2月1日

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  • A. D. Chernyshov,
  • O. Yu. Nikiforova,
  • V. V. Goryainov,
  • M. I. Popov

摘要

Abstract

Fundamentals of fast universal discrete orthogonal trigonometric interpolations for non-periodic functions are presented enabling highly accurate approximate solution of differential problems to be obtained. Using the method of fast universal discrete orthogonal trigonometric interpolations and extrapolations, an approximate analytical solution to the problem of finding the trajectory of a flying vehicle is obtained, and the coordinates of its rendezvous with another flying vehicle are determined. Numerical experiments showed that in the test problem under consideration where the flying vehicle trajectories are described by low-degree polynomials, the relative error in finding the coordinates does not exceed 0.1%, and the calculation time does not exceed 25 seconds.