Asymptotic behavior of the solution of the integral boundary value problem for singularly perturbed integro-differential equations

Abstract

The work is devoted to clarifying asymptotic with respect to a small parameter behavior of the solution of the integral boundary value problem for singularly perturbed linear integro-differential equation. In the work are obtained analytical formula and asymptotic estimates of the solution for the integral boundary value problem. It is established that the solution of the considered boundary value problem at the ends of a given segment has the phenomena of boundary jumps of the same orders. A modified degenerate boundary value problem is constructed, to the solution of which approaches the solution of assumed singularly perturbed integral boundary value problem. The value of the jump of integral terms is found.