论文标题
迭代转换方法
The Iterative Transformation Method
论文作者
论文摘要
在转换方法中，通过解决一个或多个相关的初始值问题来获得给定边界值问题的数值解决方案。因此，转换方法（如拍摄方法）是一种初始值方法。转换和拍摄方法之间的主要区别在于，前者是从缩放不变理论中构思并得出其表述的。本文涉及迭代转换方法在边界层理论中的几个问题中的应用。迭代方法是t {Ö} pfer的非著作算法的扩展，作为解决著名的布拉西乌斯问题的简单方法。这种迭代方法为解决方案的存在和独特性提供了简单的数值测试。在这里，我们展示了该方法如何应用于无穷大的均质边界条件的问题，尤其是我们解决了边界层理论的Sakiadis问题。此外，我们展示了如何将我们的方法与牛顿的词根搭配。获得的数值结果与文献中可用的结果相比良好。这里的主要目的是，为Blasius或Sakiadis开发的任何方法，问题都可能扩大到更具挑战性或有趣的问题。在这种情况下，最近已应用迭代转换方法来计算Falkner-Skan模型的Stewartson的正常和反向流解决方案[Comput。 \＆Fluids，{\ bf 73}（2013）pp。202-209]。
In a transformation method, the numerical solution of a given boundary value problem is obtained by solving one or more related initial value problems. Therefore, a transformation method, like a shooting method, is an initial value method. The main difference between a transformation and a shooting method is that the former is conceived and derive its formulation from the scaling invariance theory. This paper is concerned with the application of the iterative transformation method to several problems in the boundary layer theory. The iterative method is an extension of the T{ö}pfer's non-iterative algorithm developed as a simple way to solve the celebrated Blasius problem. This iterative method provides a simple numerical test for the existence and uniqueness of solutions. Here we show how the method can be applied to problems with a homogeneous boundary conditions at infinity and in particular we solve the Sakiadis problem of boundary layer theory. Moreover, we show how to couple our method with Newton's root-finder. The obtained numerical results compare well with those available in the literature. The main aim here is that any method developed for the Blasius, or the Sakiadis, problem might be extended to more challenging or interesting problems. In this context, the iterative transformation method has been recently applied to compute the normal and reverse flow solutions of Stewartson for the Falkner-Skan model [Comput. \& Fluids, {\bf 73} (2013) pp. 202-209].
