半无限区间上边值问题的自由边界列式
Free Boundary Formulation for Boundary Value Problems on Semi-Infinite Intervals: An up to Date Review
摘要：
在本文中，我们提出了一个审查的自由边界制定BVP定义在半无限区间。为了读者的方便，我们用一类二阶边值问题来说明本文的主要思想和定理。此外，我们能够显示所提出的方法的有效性，使用两个例子中的精确解都为BVP和他们的\FBF \是可用的。然后，我们描述的自由边界制定的一般类的BVP的$n$阶微分方程。在这方面，我们报告三个问题解决使用自由边界制定。用迭代变换法或Keller二阶有限差分法得到的数值结果与文献中的结果吻合得很好。本研究的最后一个结果是，为了引导感兴趣的读者，我们提供了一个广泛的参考书目。当然，我们可以在未来的方面进一步和更有趣的应用的自由边界制定。
英文摘要：
In this paper, we propose a review of the free boundary formulation for BVPs defined on semi-infinite intervals. The main idea and theorem are illustrated, for the reader convenience, by using a class of second-order BVPs. Moreover, we are able to show the effectiveness of the proposed approach using two examples where the exact solution both for the BVPs and their \FBF \ are available. Then, we describe the free boundary formulation for a general class of BVPs governed by an $n$-order differential equation. In this context, we report three problems solved using the free boundary formulation. The reported numerical results, obtained by the iterative transformation method or Keller's second-order finite difference method, are found to be in very good agreement with those available in the literature. The last result of this research is that, in order to orient the interested reader, we provide an extensive bibliography. Of course, we may aspect further and more interesting applications of the free boundary formulation in the future.
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