论文标题
在半无限时间间隔内为边界价值问题的自由边界公式：最新评论
Free Boundary Formulation for Boundary Value Problems on Semi-Infinite Intervals: An up to Date Review
论文作者
论文摘要
在本文中，我们提出了对在半无限间隔定义的BVP的自由边界公式的综述。通过使用一类二阶BVP来说明主要思想和定理，以便读者的便利性。此外，我们能够使用两个示例来显示所提出的方法的有效性，其中可用的BVP和它们的\ fbf \提供了精确的解决方案。然后，我们描述了由$ n $订单微分方程控制的一般BVP的免费边界公式。在这种情况下，我们报告了使用自由边界公式解决的三个问题。发现通过迭代转换方法或凯勒的二阶有限差异方法获得的数值结果与文献中的可用差异非常吻合。这项研究的最后结果是，为了确定感兴趣的读者，我们提供了广泛的书目。当然，我们可能会在将来进一步方面的自由边界表述的更有趣的应用。
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.
