Abstract:
A linear two-point boundary value problem for a system of loaded differential equations with
impulse effect
is investigated. The parameterization method is used to solve the problem. The essence of
parameterization method is that segment, where the loaded differential equation is considered, is
divided into parts by loading points, and the initial problem is reduced to the boundary value
problem with a parameter. The solution to boundary value problem with parameter is defined as a
limit of systems sequence, consisting of the pairs of parameter and function. Parameters are
defined by a system of linear algebraic equations. System of linear algebraic equations is
determined by the matrices of boundary conditions, the system of loaded differential equations, and
the conditions of impulse effect. An algorithm for finding the solution to linear two-point
boundary value problem for the systems of loaded differential equations with impulse effect is
offered. The convergence conditions of the algorithm providing the existence and uniqueness of
solution to the considered problem are established. Sufficient conditions for unique solvability of
the problem in the
terms of initial data are received.
