Numerical Solution of Two Point Boundary Value Problems
Numerical Solution of Two Point Boundary Value Problems
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DOI：
10.1137/1.9781611970449
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发表时间：
1976
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影响因子：
--
通讯作者：
H. Keller
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文献类型：
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作者：
H. Keller
这本专著是一个帐户的十个讲座我提出的区域研究会议上的数值解两点边值问题。会议在德州理工大学举行。1975年7月7日至11日，大学，是由国家科学基金会支持和数学科学会议委员会管理的系列之一。我利用这个机会，部分地，增加和更新以前关于这个问题的专著的部分。然而，由于讲座只能是该领域的部分调查，许多有趣的主题不得不被省略。事实上，省略的内容构成了该领域另一次会议的基础。它们包括：自动网络选择、奇异扰动问题、分叉问题、最优控制问题、完成差分格式以产生不变嵌入方案、Galerkin方法、配置（与分段多项式以外的方法）、奇异非线性问题以及毫无疑问的其他重要主题。然而，主题的主要核心是涵盖相当广泛，并已包括一些证据时，他们是简短的，有助于更好地理解。相当多的新材料被覆盖，许多需要研究的领域被暴露。很高兴感谢保罗纳尔逊教授和他的委员会的其他成员组织了这次非常好的会议。与会者是一个最令人兴奋的群体，我的讲座的任何成功都要归功于聚会的普遍精神。美国国家科学基金会在支持地区会议系列方面提供了最有用和最具创新性的服务，我很荣幸能成为这次会议的首席讲师。多年来，我在这一领域的大部分研究都是由美国陆军研究办公室（达勒姆）根据合同DAHC 04-68-C-0006和能源研究与发展管理局根据合同AT（04-3-767）项目协议12赞助的。最后，我想感谢帕姆·哈根，感谢她在准备出版这份手稿的艰巨任务中给予的愉快帮助。赫伯特B。KellerPasadena八月1975
This monograph is an account of ten lectures I presented at the Regional Research Conference on Numerical Solution of Two-Point Boundary Value Problems. The Conference was held at Texas Tech. University on July 7–11, 1975, and was one of a series supported by the National Science Foundation and managed by the Conference Board of the Mathematical Sciences.I have used this opportunity, in part, to augment and bring up to date portions of a previous monograph on this subject [24]. However, as the lectures could only be a partial survey of the field, many interesting topics had to be omitted Indeed the omissions form the basis for another conference in this area. They include: automatic net selection, singular perturbation problems, bifurcation problems, optimal control problems, the completion of difference schemes to yield invariant embedding schemes, Galerkin methods, collocation (with other thanpiecewise polynomials), singular nonlinear problems and no doubt other significant topics. However, the main core of the subject is covered rather broadly and some proofs have been included when they are brief and contribute to a better understanding. Quite a bit of new material is covered and numerous areas in need of study are exposed.It is a pleasure to thank Professor Paul Nelson and the rest of his committee for organizing this very well-run conference. The participants were a most stimulating group and any success of my lectures was due in no small part to the general spirit of the gathering. The National Science Foundation is performing a most useful and innovative service in supporting the Regional Conference Series and I was honored to have been the principal lecturer at this one. Much of my research in this area has been sponsored over the years by the U.S. Army Research Office (Durham) under Contract DAHC 04-68-C-0006 and by the Energy Research and Development Administration under Contract AT(04-3-767) Project Agreement 12. Finally I wish to thank Pam Hagan for her cheerful help in the arduous task of preparing this manuscript for publication.Herbert B. KellerPasadenaAugust1975