Abstract
In this paper, we investigate a boundary value problem with a parameter for an impulsive integro-differential equations involving integral constraints. To solve the problem, we employ the Dzhumabaev parametrization method in combination with numerical techniques. By introducing additional parameters, the original boundary value problem is reduced to an equivalent system of linear algebraic equations. The coefficients and the right-hand side of this system are computed by solving Cauchy problems for ordinary differential equations on subintervals. Furthermore, sufficient conditions for the existence and uniqueness of the solution to the boundary value problem with a parameter are established. Based on the obtained theoretical results, we develop a constructive numerical method and propose algorithms for its implementation. The efficiency of the presented approach is emonstratedthrough numerical example.