Projector Approach to Constructing the Asymptotics of Solution of Initial Value Problems for Weakly Nonlinear Discrete Systems with Small Step in the Critical Case

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Abstract

An algorithm for constructing an asymptotic solution containing boundary functions for an initial value problem for a weakly nonlinear system of discrete equations with small step in the critical case under certain conditions is given in the article by V.F. Butuzov and A.B. Vasil’eva in Differ. Uravn., 1970, vol. 6, no. 4, pp. 650–664. In the present paper, orthogonal projectors are used to construct the asymptotics of the solution of this problem. This projector approach greatly simplifies the understanding of the algorithm for constructing the asymptotics and permits explicitly writing the problems from which one can find the terms of any order in the asymptotics of the solution.

About the authors

G. A Kurina

Voronezh State University, Voronezh, 394018, Russia; Federal Research Center “Computer Science and Control,” Russian Academy of Sciences, Moscow, 119333, Russia

Email: kurina@math.vsu.ru
г. Воронеж, Россия;г. Москва, Россия

Nguen Tkhi Khoay

VNU University of Science, Vietnam National University, Ha Noi, Viet Nam

Author for correspondence.
Email: nguyenthihoai@hus.edu.vn
г. Ханой, Вьетнам

References

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