一类常微分方程控制的自由边界值问题的非迭代变换方法
A Non-Iterative Transformation Method for a Class of Free Boundary Value Problems Governed by ODEs
摘要：
本文的目的是指出由二阶自治常微分方程所支配的自由边界问题可以转化为初值问题。自由边界问题的数值解引起了人们的兴趣，因为这些问题总是非线性的。本文的理论内容是原始的：已经在文献中的结果有关的不变性性质的缩放或螺旋群的点变换，但在这里，我们展示了如何也可以使用E不变性性质的平移群。我们测试所提出的算法，通过解决三个问题：一个问题描述的绳索配置对障碍物，一个动态问题与非线性力，和一个问题有关的最佳长度估计管式流动反应器。
英文摘要：
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.
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。
