Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations

by K.E. Brenan

Many physical problems are most naturally described by systems ofdifferential and algebraic equations. This book describes some of theplaces where differential-algebraic equations (DAEs) occur. The basicmathematical theory for these equations is developed and numericalmethods are presented and analyzed. Examples drawn from a variety ofapplications are used to motivate and illustrate the concepts andtechniques.This book, originally published in 1989 and updated and expanded forthe Classics edition, is the only general DAE book available. It notonly develops guidelines for choosing different numerical methods, itis the first book to discuss DAE codes, including the popular DASSLcode. An extensive discussion of backward differentiation formulasdetails why they have emerged as the most popular and best understoodclass of linear multistep methods for general DAEs. New to thisedition is a chapter that brings the discussion of DAE software up todate.The objective of this monograph is to advance and consolidate theexisting research results for the numerical solution of DAEs. Theauthors present results on the analysis of numerical methods and alsoshow how these results are relevant for the solution of problems fromapplications. They develop guidelines for problem formulation andeffective use of the available mathematical software and provideextensive references for further study.AudienceEngineers, physicists, and other scientists who must solve DAEs;numerical analysts; and applied mathematicians will find thismonograph both useful and informative.About the AuthorsKathryn E. Brenan is Engineering Specialist at The AerospaceCorporation. Stephen L. Cambell is Professor, Department ofMathematics, North Carolina State University, Raleigh. Linda R.Petzold is Professor, Department of Computer Science, University ofMinnesota, Minneapolis.

Hardcover

First published January 1, 1987