Solving Ordinary Differential Equations II : Stiff and Differential - Algebraic Problems.
- 1st ed.
- 1 online resource (615 pages)
- Springer Series in Computational Mathematics Series ; v.14 .
- Springer Series in Computational Mathematics Series .
Springer Series in Computational Mathematics 14 -- Solving Ordinary Differential Equations II -- Copyright -- Preface -- Contents -- Chapter IV. Stiff Problems - One-Step Methods -- IV.1. Examples of Stiff Equations -- IV.2. Stability Analysis für Explicit RK Methods -- IV.3. A-Stable Runge-Kutta 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 Differential Aigebraic Equations -- VI.1. Singular Perturbation and Index 1 Problems -- VI.2. Epsilon Expansions for Exact and RK Solutions -- VI.3. Rosenbrock Methods -- VI.4. Extrapolation Methods -- VI.5. Higher Index Problems -- VI.6. Multistep Methods for Index 2 DAE -- VI.7. Runge-Kutta Methods for Index 2 DAE -- VI.8. Order Conditions for Index 2 DAE -- VI.9. Computation of Multibody Mechanisms -- Appendix. Fortran Codes -- Bibliography -- Symbol Index -- Subject Index.