ASYMPTOTIC SOLUTION OF THE PERTURBED PROBLEM WITH A REGULARLY SINGULAR POINT

Abstract

A uniform asymptotic expansion of the solution of the two-point Dirichlet boundary value problem for a linear inhomogeneous ordinary differential equation of the second order with a small parameter at the highest derivative is constructed on the segment. The peculiarity of the problem under consideration is that the corresponding unperturbed problem for an ordinary differential equation of the first order has a regular singular point at the left end of the segment. We propose a simpler algorithm for constructing an asymptotic solution to boundary value problems, which consists of two composite functions, and our boundary functions constructed in the neighborhood of a singular point have the “boundary layer” property, i.e. power-law disappear outside the boundary layer.