Asymptotic convergence of the solution for singularly perturbed boundary value problem with boundary jumps

Abstract

The article is devoted to study of boundary value problem with boundary jumps for third order linear integro-di˙erential equation with a small parameter at the highest derivatives, provided that additional characteristic equation􀀁s roots have opposite signs. The modified unperturbed boundary value problem is constructed. The solution of modified unperturbed problem is obtained. Initial jumps􀀁 values of the integral term and solution are defined. An estimate di˙erence of solution for singularly perturbed and modified unperturbed boundary value problems is obtained. The convergence of solution for singularly perturbed boundary value problem to solution of modified unperturbed boundary value problem is proved.