Abstract. We consider the two-point boundary value problem for the singularly perturbed higher order linear integro-differential equation. The initial jumps of solutions and integral terms are proved. The constructive formulae and asymptotic estimations for solutions and their derivatives are obtained.

In this article we constructed an asymptotic expansion of the solution undivided boundary value problem for singularly perturbed integro-differential equations with an initial jump phenomenon m – th order. We obtain the theorem about estimation of the remainder term’s asymptotic with any degree of accuracy in the smallparameter.

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Construction of the solution of the boundary value problem for integro differential equation with a small parameter in highest derivativesThe article is devoted to the study analytical formula of solution of boundary value problem with initial jump for a linear integro-differential equation of n + m order with a small parameter in the highest derivatives. In this paper singular perturbed homogeneous differential equation of n+m order are constructed fundamental system of solutions. With the fundamental system of solutions are constructed Cauchy function and boundary functions. Using Cauchy function and boundary functions are obtained explicit analytical formula of solution of considered local boundary value problem for singular perturbed integro-differential equation of high order.

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