Ernst Hairer, Gerhard Wanner

Solving Ordinary Differential Equations II (eBook, PDF)

Stiff and Differential-Algebraic Problems

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 614
• Erscheinungstermin: 10. März 2010
• Englisch
• ISBN-13: 9783642052217
• Artikelnr.: 53085416

Autorenporträt

Ernst Hairer, University of Geneva, Switzerland / Gerhard Wanner, University of Geneva, Switzerland

Inhaltsangabe

IV. Stiff Problems - One-Step Methods.- IV.1 Examples of Stiff Equations.- IV.2 Stability Analysis for Explicit RK Methods.- IV.3 Stability Function of Implicit RK-Methods.- IV.4 Order Stars.- IV.5 Construction of Implicit Runge-Kutta Methods.- IV.6 Diagonally Implicit RK Methods.- IV.7 Rosenbrock-Type Methods.- IV.8 Implementation of Implicit Runge-Kutta Methods.- IV.9 Extrapolation Methods.- IV.10 Numerical Experiments.- IV.11 Contractivity for Linear Problems.- IV.12 B-Stability and Contractivity.- IV.13 Positive Quadrature Formulas and B-Stable RK-Methods.- IV.14 Existence and Uniqueness of IRK Solutions.- IV.15 B-Convergence.- V. Multistep Methods for Stiff Problems.- V.1 Stability of Multistep Methods.- V.2 "Nearly" A-Stable Multistep Methods.- V.3 Generalized Multistep Methods.- V.4 Order Stars on Riemann Surfaces.- V.5 Experiments with Multistep Codes.- V.6 One-Leg Methods and G-Stability.- V.7 Convergence for Linear Problems.- V.8 Convergence for Nonlinear Problems.- V.9 Algebraic Stability of General Linear Methods.- VI. Singular Perturbation Problems and Index 1 Problems.- VI.1 Solving Index 1 Problems.- VI.2 Multistep Methods.- VI.3 Epsilon Expansions for Exact and RK Solutions.- VI.4 Rosenbrock Methods.- VI.5 Extrapolation Methods.- VI.6 Quasilinear Problems.- VII. Differential-Algebraic Equations of Higher Index.- VII.1 The Index and Various Examples.- VII.2 Index Reduction Methods.- VII.3 Multistep Methods for Index 2 DAE.- VII.4 Runge-Kutta Methods for Index 2 DAE.- VII.5 Order Conditions for Index 2 DAE.- VII.6 Half-Explicit Methods for Index 2 Systems.- VII.7 Computation of Multibody Mechanisms.- VII.8 Symplectic Methods for Constrained Hamiltonian Systems.- Appendix. Fortran Codes.- Driver for the Code RADAU5.- Subroutine RADAU5.- SubroutineRADAUP.- Subroutine RODAS.- Subroutine SEULEX.- Problems with Special Structure.- Use of SOLOUT and of Dense Output.- Symbol Index.

Rezensionen

This is a superb book...Throughout, illuminating graphics, sketches and quotes from papers of researchers in the field add an element of easy informality and motivate the text." Mathematics Today.

From the reviews of the second edition:

This is a superb book...Throughout, illuminating graphics, sketches and quotes from papers of researchers in the field add an element of easy informality and motivate the text." Mathematics Today

"This volume, on nonstiff equations, is the second of a two-volume set. This second volume treats stiff differential equations and differential-algebraic equations. ... This book is highly recommended as a text for courses in numerical methods for ordinary differential equations and as a reference for the worker. It should be in every library, both academic and industrial." (Teodora-Liliana Radulescu, Zentralblatt MATH, Vol. 1192, 2010)