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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| Main Authors: | , |
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| Corporate Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg :
Springer Berlin Heidelberg : Imprint: Springer,
1996.
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| Edition: | 2nd ed. 1996. |
| Series: | Springer Series in Computational Mathematics,
14 Springer eBook Collection. |
| Subjects: | |
| 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.