Umfang:
Online-Ressource (XVI, 614p. 137 illus, digital)
ISBN:
9783642052217
Serie:
Springer Series in Computational Mathematics 14
Inhalt:
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.
Inhalt:
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 problems, a third on the treatment of singular perturbation problems, and a last one on differential-algebraic problems with applications to constrained mechanical systems. The beginning of each chapter is of introductory nature, followed by practical applications, the discussion of numerical results, theoretical investigations on the order and accuracy, linear and nonlinear stability, convergence and asymptotic expansions. Stiff and differential-algebraic problems arise everywhere in scientific computations (e.g. in physics, chemistry, biology, control engineering, electrical network analysis, mechanical systems). Many applications as well as computer programs are presented. Ernst Hairer and Gerhard Wanner were jointly awarded the 2003 Peter Henrici Prize at ICIAM 2003 in Sydney, Australia.
Weitere Ausg.:
ISBN 9783642052200
Weitere Ausg.:
Buchausg. u.d.T. Solving ordinary differential equations ; 2: Stiff and differential algebraic problems Berlin : Springer, 2010 ISBN 9783642052200
Weitere Ausg.:
ISBN 9783540604525
Sprache:
Englisch
Fachgebiete:
Mathematik
DOI:
10.1007/978-3-642-05221-7
URL:
Volltext
(lizenzpflichtig)
URL:
Volltext
(lizenzpflichtig)
Mehr zum Autor:
Hairer, Ernst 1949-
Mehr zum Autor:
Wanner, Gerhard 1942-
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