On a method of approximation of solutions to delay differential equations

Abstract

Connections between solutions to a class of systems of ordinary differential equations of a large dimension and delay equations are studied. A new method is justified for approximation of solutions to delay equations.In the bunch of the articles [1-5], new connections were established between solutions to delay differential equations of the formand solutions to some systems of ordinary differential equations of a large dimension n of the formThese connections allow us to study the qualitative properties of solutions to (1.1) by the theoretical results established for (1.2) and to determine approximate solutions to (1.2) by solving boundary value problems for (1.1) numerically.In the present article we continue [1][2][3][4][5] and examine the delay differential equation of the formAs shown in [1], this equation is closely related to the system of differential equations (1.2), where

On the properties of solutions to a class of nonlinear systems of differential equations of large dimension

“…The result yields a rigorous mathematical justification of a method for numerically finding the concentration of the final product x n (t) for n 1 by using the delay equation. Theorem 1 is a starting point for deriving similar statements for various systems of ordinary differential equations (see [5][6][7][8][9][10][11][12][13][14][15][16][17] for instance). G. V. Demidenko proposed a series of methods for proving direct and inverse limit theorems which relate the solutions to classes of systems of nonlinear ordinary differential equations of large dimension and generalized solutions to delay equations.…”