symptotic convergence of solution of boundary problems for the singular perturbated integro-differential equations

Abstract

In this work boundary value problem for the singular perturbed linear integral differential equations of nth order. Estimates of the solution and its derivatives of this problem are received. Established that the solution of the boundary value problem at the point t = 0 has the phenomenon of initial jump (n-2) th order. Changed unperturbed boundary value problem is constructed. Solution of the given singular perturbed boundary value problem tends to the solution of the changed unperturbed boundary value problem. Changed unperturbed boundary value problem is different from the usual unperturbed problem. There are initial jump of the solution and integral member. Estimates of the difference between the solutions of the given singular perturbed and unperturbed changed problems are received. Values of initial jumps of the solution and of the integral member are found.