Solving Ordinary Differential Equations II Stiff and Differential-Algebraic Problems / by Ernst Hairer, Gerhard Wanner.

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 pro...

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Bibliographic Details
Main Authors: Hairer, Ernst. (Author,, Wanner, Gerhard. (
Corporate Author: SpringerLink (Online service)
Format: eBook
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1996.
Edition:2nd ed. 1996.
Series:Springer Series in Computational Mathematics, 14
Springer eBook Collection.
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
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.