In this paper we consider a class of boundary value problems for third order nonlinear functional differential equation. By the reduction of the problem to operator 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 total error. Some examples demonstrate the validity of the obtained theoretical results and the efficiency of the numerical method. The approach used for the third order nonlinear functional differential equation can be applied to functional differential equations of any orders.
翻译：在本文中,我们考虑的是第三顺序非线性功能差异方程式的边界值问题类别。通过将问题降低到操作方程式,我们确定解决方案的存在和独特性,并构建一个数字方法来解决它。我们证明该方法为第二顺序准确度,并获得总误差的估计值。一些例子显示了获得的理论结果的有效性和数字方法的效率。第三顺序非线性功能差异方程式所使用的方法可以适用于任何订单的功能差异方程式。
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