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.

翻译：本文采用参数化方法研究了一类Fredholm积分微分方程组的多点边值问题。我们独立研究了退化核情形，推导了该情形的适定性条件，并提出了求解近似解与数值解的若干算法。进而，本文建立了Fredholm积分微分方程组多点问题适定性的充要条件，并开发了若干求解其近似解的算法。这些算法基于退化核积分微分方程组近似问题的解。