Quasi-Newton Methods for Discretized Non-linear Boundary Problems
Quasi-Newton Methods for Discretized Non-linear Boundary Problems
复制标题
离散非线性边界问题的拟牛顿法
DOI：
10.1093/imamat/11.3.351
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发表时间：
1973
影响因子：
1.2
通讯作者：
S. Soul
中科院分区：
文献类型：
--
作者：
W. Hart;S. Soul
非线性边值问题的离散化一般会导致一个有限的非线性代数方程组，可以预料到后者在边值问题和离散化方法上都具有特殊的结构。代数系统的数值解是一个严重的数值问题，本文的重点是指出，在某些重要的情况下，可以构造特殊用途的拟牛顿方法。我们以一个用配置离散化的非线性微分方程为例进行了说明，并给出了实验结果，实验结果表明，这种特殊的方法可以改善性能。
The discretization of non-linear boundary problems generally leads to a finite system of non-linear algebraic equations, and it is to be expected that this latter has special structure arising both from the boundary problem and the method of discretization used. The numerical solution of the algebraic system represents a serious numerical problem, and it is the point of this paper to indicate that, in certain important cases, special purpose quasi-Newton methods can be constructed. We illustrate by considering a single nonlinear differential equation discretized by collocation and present experimental results which indicate that an improvement in performance can be expected from the special methods.