论文标题
由ODES控制的一类自由边界价值问题类别的非题转换方法
A Non-Iterative Transformation Method for a Class of Free Boundary Value Problems Governed by ODEs
论文作者
论文摘要
这项工作的目的是指出，由二阶自动构成的普通微分方程控制的一类自由边界问题可以转化为初始价值问题。出现了对自由边界问题的数值解决方案的兴趣，因为这些始终是非线性问题。本文的理论内容是原始的：文献中已经可以使用的结果与点转换的缩放或螺旋组的不变性属性有关，但是在这里我们展示了如何使用翻译组的E不变性属性。我们通过解决三个问题来测试提出的算法：描述针对障碍物的绳索配置的问题，非线性力的动态问题以及与管状流动反应器的最佳长度估计有关的问题。
The aim of this work is to point out that the class of free boundary problems governed by second order autonomous ordinary differential equations can be transformed to initial value problems. Interest in the numerical solution of free boundary problems arises because these are always nonlinear problems. The theoretical content of this paper is original: results already available in literature are related to the invariance properties of scaling or spiral groups of point transformations but here we show how it is also possible to use e invariance properties of a translation group. We test the proposed algorithm by solving three problems: a problem describing a rope configuration against an obstacle, a dynamical problem with a nonlinear force, and a problem related to the optimal length estimate for tubular flow reactors.
