Ciarlet, Handbook of numerical analysis vol 8.. Theoretical and numerical analysis of differential-algebraic equations (Elsevier).pdf

Theoretical and Numerical
Analysis of
Differential-Algebraic
Equations
Patrick J Rabier
Departmentof Mathematics
University of Pittsburgh
Pittsburgh, PA 15260
USA
Werner C Rheinboldt
Departmentof Mathematics
University of Pittsburgh
Pittsburgh, PA 15260
USA
HANDBOOK OF NUMERICAL ANALYSIS, VOL VIII
Solution of Equations in Rn (Part 4)
Techniques of puting (Part 4)
Numerical Methods for Fluids (Part 2)
edited by P G Ciarlet and J L Lions
© 2002 Elsevier Science B V All rights reserved
183
Contents
1 Introduction 189
PART A Theoretical Basis
CHAPTER I Model Problems 197
work problems 197
3 Constrained mass-point systems 199
4 Constrained rigid-body systems 203
5 Singular perturbations 208
6 DA Es in the solution of PD Es 212
7 Control problems 214
8 Differential equations with invariants 216
CHAPTER II Linear DA Es: Classical Solutions 219
9 Linear DA Es with constant coefficients 219
10 Time-dependent coefficients 221
11 Transformation functions 223
12 Reduction of operator pairs 225
13 Classical solutions of linear DA Es 232
14 The theory of Kunkel and Mehrmann 235
15 Rectangular systems 239
16 Linear boundary value problems 241
CHAPTER III Linear DA Es: Generalized Solutions 243
17 Generalized inputs 243
18 Impulsive-smooth distributions 247
19 Discontinuous inputs 251
20 Inconsistent initial values 256
CHAPTER IV Geometric Reduction of Quasilinear DA Es 261
21 Motivation and preliminary results 262
22 Reduction procedure 264
plete reducibility and tangent vector fields 269
24 Application to DA Es 271
25 An example: The pendulum 274
26 Index one DA Es 279
185
186 Rabier and W C Rheinboldt
27 Local parametrizations 284
28 Other approaches 287
CHAPTER V Special Classes of Nonlinear DA Es 293
29 Algebraically explicit DA Es of index one 293
30 Algebraically explicit DA Es of index two 295
31 Algebraically explicit DA Es of index three 301
32 Examples 303
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