In this paper, we consider a boundary value problem (BVP) for a fourth order nonlinear functional integro-differential equation. We establish the existence and uniqueness of solution and construct a numerical method for solving it. We prove that the method is of second order accuracy and obtain an estimate for the total error. Some examples demonstrate the validity of the obtained theoretical results and the efficiency of the numerical method.

翻译：在本文中,我们考虑了第四顺序非线性功能性整形等式的边界值问题。我们确定了解决方案的存在和独特性,并构建了解决问题的数值方法。我们证明该方法为第二顺序精确度,并获得了总误差的估计值。一些例子证明了获得的理论结果的有效性和数字方法的效率。