Author | Hairer, Ernst. author |
---|---|
Title | Solving Ordinary Differential Equations II [electronic resource] : Stiff and Differential-Algebraic Problems / by Ernst Hairer, Gerhard Wanner |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1996 |
Edition | Second Revised Edition |
Connect to | http://dx.doi.org/10.1007/978-3-642-05221-7 |
Descript | XV, 614 p. online resource |
IV. Stiff Problems โ 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 โNearlyโ 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