The subject of this book is the solution of stiff differential equations and of differential-algebraic systems (differential equations with constraints). There is a chapter on one-step and extrapolation methods for stiff problems, another on multistep methods and general linear methods for stiff problems, a third on the treatment of singular perturbation problems, and a last one on differential-algebraic problems with applications to constrained mechanical systems. The beginning of each chapter is of introductory nature, followed by practical applications, the discussion of numerical results, theoretical investigations on the order and accuracy, linear and nonlinear stability, convergence and asymptotic expansions. Stiff and differential-algebraic problems arise everywhere in scientific computations (e.g. in physics, chemistry, biology, control engineering, electrical network analysis, mechanical systems). Many applications as well as computer programs are presented.
Ernst Hairer and Gerhard Wanner were jointly awarded the 2003 Peter Henrici Prize at ICIAM 2003 in Sydney, Australia.
Author(s): Ernst Hairer, Gerhard Wanner (auth.)
Series: Springer Series in Computational Mathematics 14
Edition: 2
Publisher: Springer-Verlag Berlin Heidelberg
Year: 1996
Language: English
Pages: 614
Tags: Numerical Analysis;Analysis;Theoretical and Computational Chemistry;Mathematical Methods in Physics;Numerical and Computational Physics;Appl.Mathematics/Computational Methods of Engineering
Front Matter....Pages I-XV
Front Matter....Pages 1-1
Examples of Stiff Equations....Pages 2-14
Stability Analysis for Explicit RK Methods....Pages 15-39
Stability Function of Implicit RK-Methods....Pages 40-50
Order Stars....Pages 51-70
Construction of Implicit Runge-Kutta Methods....Pages 71-90
Diagonally Implicit RK Methods....Pages 91-101
Rosenbrock-Type Methods....Pages 102-117
Implementation of Implicit Runge-Kutta Methods....Pages 118-130
Extrapolation Methods....Pages 131-142
Numerical Experiments....Pages 143-166
Contractivity for Linear Problems....Pages 167-179
B-Stability and Contractivity....Pages 180-200
Positive Quadrature Formulas and B-Stable RK-Methods....Pages 201-214
Existence and Uniqueness of IRK Solutions....Pages 215-224
B-Convergence....Pages 225-238
Front Matter....Pages 239-239
Stability of Multistep Methods....Pages 240-249
“Nearly” A-Stable Multistep Methods....Pages 250-260
Generalized Multistep Methods....Pages 261-278
Order Stars on Riemann Surfaces....Pages 279-299
Experiments with Multistep Codes....Pages 300-304
Front Matter....Pages 239-239
One-Leg Methods and G-Stability....Pages 305-320
Convergence for Linear Problems....Pages 321-338
Convergence for Nonlinear Problems....Pages 339-355
Algebraic Stability of General Linear Methods....Pages 356-370
Front Matter....Pages 371-371
Solving Index 1 Problems....Pages 372-381
Multistep Methods....Pages 382-387
Epsilon Expansions for Exact and RK Solutions....Pages 388-406
Rosenbrock Methods....Pages 407-425
Extrapolation Methods....Pages 426-441
Quasilinear Problems....Pages 442-449
Front Matter....Pages 451-451
The Index and Various Examples....Pages 452-467
Index Reduction Methods....Pages 468-480
Multistep Methods for Index 2 DAE....Pages 481-491
Runge-Kutta Methods for Index 2 DAE....Pages 492-505
Order Conditions for Index 2 DAE....Pages 506-518
Half-Explicit Methods for Index 2 Systems....Pages 519-529
Computation of Multibody Mechanisms....Pages 530-542
Symplectic Methods for Constrained Hamiltonian Systems....Pages 543-563
Back Matter....Pages 565-614
