ON MATHEMATICAL MODELING OF (NANO) TECHNOLOGIES RELATED TO NAVIGATION PROBLEMS ON THE BASE OF GENERALIZATIONS OF THE PICARD METHOD

Authors

  • N. M. Glazunov National Aviation University, Kyiv

DOI:

https://doi.org/10.18372/1990-5548.57.13247

Keywords:

Picard method, ordinary differential equation, iterated integral, hyperlogarithm, nanotechnology, Picard–Fuchs differential equation, multiple zeta value

Abstract

The aim of the paper is the mathematical modeling of nanotechnology problems of navigation based on generalizations of the Picard method. The Picard method for solving systems of ordinary differential equations, and its extensions on the basis of hyperlogarithms  and iterated path integrals, are presented. The derivation of the Picard-Fuchs differential equations for connections in bundles on schemes is given. The results can be used to study the corresponding differential equations and to calculate the Taylor coefficients of (dimensionally regularized) Feynman amplitudes with rational parameters.

Author Biography

N. M. Glazunov, National Aviation University, Kyiv

Department of Electronics

Doctor of Phys.-Math. Sciences. Senior researcher. Professor

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Issue

Vol. 3 No. 57 (2018)

Section

MATHEMATICAL MODELING OF PROCESSES AND SYSTEMS

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