Solving Finite Difference Approximations to Nonlinear Two-Point Boundary Value Problems by a Homotopy Method
Solving Finite Difference Approximations to Nonlinear Two-Point Boundary Value Problems by a Homotopy Method
复制标题
用同伦法求解非线性两点边值问题的有限差分近似
DOI：
10.1137/0901034
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发表时间：
1980
期刊：
影响因子：
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通讯作者：
L. Watson
中科院分区：
文献类型：
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作者：
L. Watson
Chow-Yorke算法是一种同伦方法，已被证明全局收敛于Brouwer不动点问题，零发现类，非线性规划和两点边值问题。该方法具有数值稳定性，并已成功应用于几个实际的非线性优化和流体动力学问题。同伦方法以前应用于两点边值问题的基础上拍摄，这是不合适的尖锐边界层的流体动力学问题。本文证明了非线性两点边值问题的一类有限差分逼近的Chow-Yorke算法的全局收敛性。文中简要介绍了该算法的数值实现，并给出了两个相当困难的流体力学边值问题的计算结果。
The Chow–Yorke algorithm is a homotopy method that has been proved globally convergent for Brouwer fixed point problems, classes of zero finding, nonlinear programming, and two-point boundary value problems. The method is numerically stable, and has been successfully applied to several practical nonlinear optimization and fluid dynamics problems. Previous application of the homotopy method to two-point boundary value problems has been based on shooting, which is inappropriate for fluid dynamics problems with sharp boundary layers. Here the Chow–Yorke algorithm is proved globally convergent for a class of finite difference approximations to nonlinear two-point boundary value problems. The numerical implementation of the algorithm is briefly sketched, and computational results are given for two fairly difficult fluid dynamics boundary value problems.