  In the present paper, we study a multipoint boundary value problem for a
system of Fredholm integro-differenial equations by the method of
parameterization. The case of a degenerate kernel is studied separately, for
which we obtain well-posedness conditions and propose some algorithms to find
approximate and numerical solutions to the problem. Then we establish necessary
and sufficient conditions for the well-posedness of the multipoint problem for
the system of Fredholm integro-differential equations and develop some
algorithms for finding its approximate solutions. These algorithms are based on
the solutions of an approximating problem for the system of
integro-differential equations with degenerate kernel.
