ON MATHEMATICAL MODELING OF (NANO) TECHNOLOGIES RELATED TO NAVIGATION PROBLEMS ON THE BASE OF GENERALIZATIONS OF THE PICARD METHOD - Glazunov, N. M. (Electronics and Control Systems, 2018)
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.