Chapter IV. Stiff Problems--One-step Methods
IV.1 Examples of Stiff Equations
IV.2 Stability Analysis for Explicit RK Methoods
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
Chapter 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
Chapter 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
Chapter 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
Bibliography
Symbol Index
Subject Index |
