Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems / Edition 2

Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems / Edition 2

by Ernst Hairer, Gerhard Wanner
     
 

ISBN-10: 3540604529

ISBN-13: 9783540604525

Pub. Date: 03/19/2004

Publisher: Springer Berlin Heidelberg

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

…  See more details below

Overview

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

Product Details

ISBN-13:
9783540604525
Publisher:
Springer Berlin Heidelberg
Publication date:
03/19/2004
Series:
Springer Series in Computational Mathematics, #14
Edition description:
2nd ed. 1996. Corr. 3rd printing 2004
Pages:
614
Product dimensions:
6.10(w) x 9.25(h) x 0.36(d)

Table of Contents

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.

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