Computer methods for ordinary differential equations and differential-algebraic equations
Computer methods for ordinary differential equations and differential-algebraic equations
复制标题
DOI：
10.1137/1.9781611971392
复制
发表时间：
1998-07
期刊：
影响因子：
--
通讯作者：
U. Ascher;L. Petzold
中科院分区：
文献类型：
--
作者：
U. Ascher;L. Petzold
来自出版商：本书专为那些想要获得现代技术实用知识的人而设计，包含微分方程数值求解课程所需的所有材料。它由该领域的两位领先权威撰写，提供了 ODE 以及微分代数方程中的初值和边值问题的统一表述。该方法旨在彻底理解实际计算的问题和方法，同时避免广泛的定理证明类型的阐述。它还解决了现有软件成功或失败的原因。本书是一本实用且内容丰富的数学导论，强调基本方法和理论、数学软件使用和开发中的问题以及科学工程应用的示例。需要大量数学发展的主题，例如哈密顿系统的辛方法，被介绍、激发并包含在练习中，但引用而不是包含完整而严格的数学演示。读者对象 本书适合以计算为重点的高年级本科生或初级研究生以及想要了解计算微分方程的实践工程师和科学家。需要学习数值分析的入门课程，学习常微分方程的入门课程会很有帮助。作者简介 Uri M. Ascher 是温哥华不列颠哥伦比亚大学计算机科学系的教授。他还是该校应用数学研究所所长。 Linda R. Petzold 是加州大学圣巴巴拉分校机械与环境工程和计算机科学系的教授。她还是该校计算科学与工程项目的主任。
From the Publisher: Designed for those people who want to gain a practical knowledge of modern techniques, this book contains all the material necessary for a course on the numerical solution of differential equations. Written by two of the field's leading authorities, it provides a unified presentation of initial value and boundary value problems in ODEs as well as differential-algebraic equations. The approach is aimed at a thorough understanding of the issues and methods for practical computation while avoiding an extensive theorem-proof type of exposition. It also addresses reasons why existing software succeeds or fails. This book is a practical and mathematically well informed introduction that emphasizes basic methods and theory, issues in the use and development of mathematical software, and examples from scientific engineering applications. Topics requiring an extensive amount of mathematical development, such as symplectic methods for Hamiltonian systems, are introduced, motivated, and included in the exercises, but a complete and rigorous mathematical presentation is referenced rather than included. Audience This book is appropriate for senior undergraduate or beginning graduate students with a computational focus and practicing engineers and scientists who want to learn about computational differential equations. A beginning course in numerical analysis is needed, and a beginning course in ordinary differential equations would be helpful. About the Authors Uri M. Ascher is a Professor in the Department of Computer Science at the University of British Columbia, Vancouver. He is also Director of the Institute of Applied Mathematics there. Linda R. Petzold is a Professor in the Departments of Mechanical and Environmental Engineering and Computer Science at the University of California at Santa Barbara. She is also Director of the Computational Science and Engineering Program there.