CONSTRUCTION OF THE ASYMPTOTICS OF A SINGULARLY PERTURBED FIRST-ORDER DIFFERENTIAL EQUATION WITH A SINGULAR POINT

Abstract

The subject of the article is a singularly perturbed homogeneous weakly linear differential equation. The purpose of the article is to find the asymptotics solving a singularly perturbed homogeneous weakly linear differential equation. To construct asymptotic, a classic asymptotic method was used - the perturbation method. Based on this method, the approximate solutions of both linear and nonlinear differential equations, and equations in private derivatives can be relatively easily. The article discusses the equation of the form  where , with the value of ε, the differential equation goes into a weakly linear ordinary equation. If the equation depends on the small parameter analytically, the solution will be presented through analytical functions. In other words, decomposes into a series of Taylor with a residual member. In the development of the classical perturbation theory, Henri Poincare, who gave an initial definition was made to the development of the classical perturbation theory. The construction of asymptotics of a singularly perturbed equation is applied, in such branches of science as: physics, technique, fluid flow and gas.