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OverviewFull Product DetailsAuthor: Ernst Hairer , Gerhard WannerPublisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K Edition: 2nd ed. 1996 Volume: 14 Dimensions: Width: 15.50cm , Height: 3.20cm , Length: 23.50cm Weight: 1.930kg ISBN: 9783642052200ISBN 10: 3642052207 Pages: 614 Publication Date: 11 March 2010 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsIV. 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.- SubroutineRADAUP.- Subroutine RODAS.- Subroutine SEULEX.- Problems with Special Structure.- Use of SOLOUT and of Dense Output.- Symbol Index.ReviewsFrom the reviews of the second edition: This is a superb book...Throughout, illuminating graphics, sketches and quotes from papers of researchers in the field add an element of easy informality and motivate the text. Mathematics Today This volume, on nonstiff equations, is the second of a two-volume set. This second volume treats stiff differential equations and differential-algebraic equations. ! This book is highly recommended as a text for courses in numerical methods for ordinary differential equations and as a reference for the worker. It should be in every library, both academic and industrial. (Teodora-Liliana RAEdulescu, Zentralblatt MATH, Vol. 1192, 2010) From the reviews of the second edition:This is a superb book...Throughout, illuminating graphics, sketches and quotes from papers of researchers in the field add an element of easy informality and motivate the text. Mathematics Today This volume, on nonstiff equations, is the second of a two-volume set. This second volume treats stiff differential equations and differential-algebraic equations. ... This book is highly recommended as a text for courses in numerical methods for ordinary differential equations and as a reference for the worker. It should be in every library, both academic and industrial. (Teodora-Liliana Radulescu, Zentralblatt MATH, Vol. 1192, 2010) This is a superb book...Throughout, illuminating graphics, sketches and quotes from papers of researchers in the field add an element of easy informality and motivate the text. Mathematics Today Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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