半无限区间上BVP的自由边界公式及非迭代变换方法
Free Boundary Formulation for BVPs on a Semi-Infinite Interval and Non-Iterative Transformation Methods
AI总结：
本文通过两个例子展示自由边界公式在半无限区间BVP中的应用，提出非迭代初始值方法以解决自由BVP，利用李群不变性理论推导方法，并应用于自由边界公式获得数值结果。
摘要：
本文研究了自由边界公式在半无限区间BVP中的应用，通过两个案例提供精确解，作为数值方法的基准。强调了如何为两类自由BVP定义非迭代初始值方法，而非传统迭代求解BVP。这些方法基于李群不变性理论推导，并应用于自由边界公式以获得有意义的数值结果。最后指出了文献中可应用这些非迭代变换方法的问题。
英文摘要：
This paper is concerned with two examples on the application of the free boundary formulation to BVPs on a semi-infinite interval. In both cases we are able to provide the exact solution of both the BVP and its free boundary formulation. Therefore, these problems can be used as benchmarks for the numerical methods applied to BVPs on a semi-infinite interval and to free BVPs. Moreover, we emphasize how for two classes of free BVPs, we can define non-iterative initial value methods, whereas BVPs are usually solved iteratively. These non-iterative methods can be deduced within Lie's group invariance theory. Then, we show how to apply the non-iterative methods to the two introduced free boundary formulations in order to obtain meaningful numerical results. Finally, we indicate several problems from the literature where our non-iterative transformation methods can be applied.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
