Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems: 14 - Rilegato

Hairer, E.

Rilegato

ISBN 10: 3540604529 ISBN 13: 9783540604525

Casa editrice: Springer Nature, 2004

Riassunto

The subject of this book is the solution of stiff differential equations and of differential-algebraic systems. This second edition contains new material including new numerical tests, recent progress in numerical differential-algebraic equations, and improved FORTRAN codes.

From the reviews:

"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

Su questo libro

Recensione:

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 Rădulescu, Zentralblatt MATH, Vol. 1192, 2010)

Contenuti:

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.- Subroutine RADAUP.- Subroutine RODAS.- Subroutine SEULEX.- Problems with Special Structure.- Use of SOLOUT and of Dense Output.- Symbol Index.

Su questa edizione

• Editore: Springer Nature
• Data di pubblicazione: 2004
• ISBN 10: 3540604529
• ISBN 13: 9783540604525
• Rilegatura: Copertina rigida
• Numero di pagine: 614