It is difficult to exactly and automatically satisfy nonseparable multipoint boundary conditions by numerical methods. With this in mind, we develop a novel algorithm to find solution for a second-order nonlinear boundary value problem (BVP), which automatically satisfies the multipoint boundary conditions prescribed. A novel concept of boundary shape function (BSF) is introduced, whose existence is proven, and it can satisfy the multipoint boundary conditions a priori. In the BSF, there exists a free function, from which we can develop an iterative algorithm by letting the BSF be the solution of the BVP and the free function be another variable. Hence, the multipoint nonlinear BVP is properly transformed to an initial value problem for the new variable, whose initial conditions are given arbitrarily. The BSF method (BSFM) can find very accurate solution through a few iterations.

中文翻译：

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非线性BVP的边界形状函数方法，自动满足规定的多点边界条件

通过数值方法难以精确地自动满足不可分离的多点边界条件。考虑到这一点，我们开发了一种新颖的算法来寻找二阶非线性边界值问题（BVP）的解决方案，该问题自动满足规定的多点边界条件。提出了一种边界形状函数（BSF）的新概念，它的存在已经得到证明，并且可以先验地满足多点边界条件。在BSF中，存在一个自由函数，我们可以通过将BSF作为BVP的解，而将自由函数作为另一个变量，来开发迭代算法。因此，将多点非线性BVP适当地转换为新变量的初始值问题，新变量的初始条件是任意给出的。