Construction of the solution of the boundary value problem for integro differential equation with a small parameter in highest derivatives

The 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.