NUMERICAL EXPERIMENTS ON ASYMPTOTICAL EQUIVALENCE OF SOLUTIONS OF EQUATIONS WITH RETARDED ARGUMENT

Abstract

Supra, the author introduced definition of asymptotical equivalence of families of functions as time tends to infinity. In the paper asymptotical behavior of solutions of initial value problems for differential equations with one bounded delay of argument as time tends to infinity is investigated. The problem to find boundaries for the coefficient providing existence of asymptotical equivalence in the space of solutions is put. To do it approximation of differential equations by difference ones and methodic of numerical experiments is proposed to be used. A system of difference equations with delay is constructed. Initial conditions and values of the coefficient are chosen randomly. The system is solved by the method of steps Boundaries for the coefficient providing asymptotical one-dimensionality of the space of solutions are found. The methodic developed can be applied to investigate asymptotical behavior of solutions of another types of initial value problems for dynamical systems.