Numerical Solution of Initial-Value Problems

Many physical problems are most naturally described by systems of differential and algebraic equations. This book describes some of the places where differential-algebraic equations (DAE's) occur. The basic mathematical theory for these equations is developed and numerical methods are presented and analyzed. Examples drawn from a variety of applications are used to motivate and illustrate the concepts and techniques. This classic edition, originally published in 1989, is the only general DAE book available. It not only develops guidelines for choosing different numerical methods, it is the first book to discuss DAE codes, including the popular DASSL code. An extensive discussion of backward differentiation formulas details why they have emerged as the most popular and best understood class of linear multistep methods for general DAE's. New to this edition is a chapter that brings the discussion of DAE software up to date.

Preface
Introduction: why DAE's?
Basic types of DAE's
applications
Overview
Theory of DAE's
Iintroduction
solvability and the index
Linear constant coefficient DAE's
Linear time varying DAE's
Nonlinear systems
Multistep methods
Introduction
DBF convergence
BDF methods, DAE's and stiff problems
General linear multistep methods
One-step methods
Introduction
Linear constant coefficient systems
Nonlinear index one systems
Semi-Explicit Nonlinear Index Two systems
Order reduction and stiffness
Extrapolation Methods
Software and DAE's
Introduction
Algorithms and Strategies in Dassl
Obtaining numerical solutions
Solving higher index systems
Applications
Introduction
Systems of rigid bodies
Trajectory prescribed path control
Electrical networks
DAE's arising from the method of lines
Bibliography
The DAE home page
Introduction
theoretical advances
Numerical analysis advancements
DAE software
DASSL
Supplementary bibliography
Index
Table of Contents provided by Publisher. All Rights Reserved.

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Numerical Solution of Initial-Value Problems in Differential Algebraic Equations

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