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Solving ordinary differential equations 2 / Ernst Hairer

Public ISBD Titre : Solving ordinary differential equations 2 : stiff and differential-algebraic problems Type de document : texte imprimé Auteurs : Ernst Hairer, Auteur ; Gerhard Wanner, Auteur Mention d'édition : 2 éd Editeur : Berlin : Springer-Verlag Année de publication : 1996 Collection : Springer series in computational mathematics num. 14 Importance : XV-614 p. Présentation : ill. Format : 25 cm ISBN/ISSN/EAN : 978-3-540-60452-5 Note générale : With 137 fig. Bibliogr. Index Langues : Anglais (eng) Mots-clés : Équations  différentielles  --  Solutions  numériques Index. décimale : 517.911 Questions générales. Théorèmes d'existence. Théorèmes d'unicité. Différentiabilité des solutions Résumé : The subject of this book is the solution of stiff differential equations and of differential-algebraic systems (differential equations with constraints). The book is divided into four chapters. 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. Note de contenu : - Stiff problems - One-step methods - Multistep methods for stiff problems - Singular perturbation problems and index 1 problems - Differential-Algebraic equations of higher index Solving ordinary differential equations 2 : stiff and differential-algebraic problems [texte imprimé] / Ernst Hairer, Auteur ; Gerhard Wanner, Auteur  . -  2 éd . - Springer-Verlag, 1996 . - XV-614 p. : ill. ; 25 cm. - (Springer series in computational mathematics; 14) . ISBN : 978-3-540-60452-5 With 137 fig. Bibliogr. Index Langues : Anglais (eng) Mots-clés : Équations  différentielles  --  Solutions  numériques Index. décimale : 517.911 Questions générales. Théorèmes d'existence. Théorèmes d'unicité. Différentiabilité des solutions Résumé : The subject of this book is the solution of stiff differential equations and of differential-algebraic systems (differential equations with constraints). The book is divided into four chapters. 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. Note de contenu : - Stiff problems - One-step methods - Multistep methods for stiff problems - Singular perturbation problems and index 1 problems - Differential-Algebraic equations of higher index

Exemplaires

Code-barres	Cote	Support	Localisation	Section	Disponibilité	Etat_Exemplaire
046790	517.911 HAI	Papier	Bibliothèque Centrale	Mathématiques	Disponible

Geometric numerical integration / Hairer , E. ; Lubich , C. ; Wanner , G.

Public ISBD Titre : Geometric numerical integration : structure-preserving algirithms for ordinary differential equations Type de document : texte imprimé Auteurs : Hairer , E., Auteur ; Lubich , C., Auteur ; Wanner , G., Auteur ; Wanner , G. Editeur : Berlin : Springer-Verlag Année de publication : 2002 Collection : Springer series in computational mathematics num. 31 Importance : XIII-515 p. Présentation : ill. Format : 25 cm ISBN/ISSN/EAN : 978-3-540-43003-2 Note générale : With 119 fig. Bibliogr. Index Langues : Anglais (eng) Mots-clés : Intégration  numérique Runge-Kutta,  Méthode  de Équations  différentielles  --  Solutions  numériques Systèmes  hamiltoniens Flots  (dynamique  différentiable) Index. décimale : 519.6 Mathématique numérique. Analyse numérique. Programmation. (informatique). Science des ordinateurs. Résumé : Numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions are the subject of this book. A complete self-contained theory of symplectic and symmetric methods, which include Runge-Kutta, composition, splitting, multistep and various specially designed integrators, is presented and their construction and practical merits are discussed. The long-time behaviour of the numerical solutions is studied using a backward error analysis (modified equations) combined with KAM theory. The book is illustrated by many figures, it treats applications from physics and astronomy and contains many numerical experiments and comparisons of different approaches. Note de contenu : - Examples and Numerical Experiments - Numerical Integrators - Order Conditions, Trees and B-Series - Conservation of First Integrals and Methods on Manifolds - Symmetric Integration and Reversibility - Symplectic Integration of Hamiltonian Systems - Further Topics in Structure Preservation - Structure-Preserving Implementation - Backward Error Analysis and Structure Preservation - Hamiltonian Perturbation Theory and Symplectic Integrators - Reversible Perturbation Theory and Symmetric Integrators - Dissipatively Perturbed Hamiltonian and Reversible Systems - Highly Oscillatory Differential Equations - Dynamics of Multistep Methods Geometric numerical integration : structure-preserving algirithms for ordinary differential equations [texte imprimé] / Hairer , E., Auteur ; Lubich , C., Auteur ; Wanner , G., Auteur ; Wanner , G. . - Springer-Verlag, 2002 . - XIII-515 p. : ill. ; 25 cm. - (Springer series in computational mathematics; 31) . ISBN : 978-3-540-43003-2 With 119 fig. Bibliogr. Index Langues : Anglais (eng) Mots-clés : Intégration  numérique Runge-Kutta,  Méthode  de Équations  différentielles  --  Solutions  numériques Systèmes  hamiltoniens Flots  (dynamique  différentiable) Index. décimale : 519.6 Mathématique numérique. Analyse numérique. Programmation. (informatique). Science des ordinateurs. Résumé : Numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions are the subject of this book. A complete self-contained theory of symplectic and symmetric methods, which include Runge-Kutta, composition, splitting, multistep and various specially designed integrators, is presented and their construction and practical merits are discussed. The long-time behaviour of the numerical solutions is studied using a backward error analysis (modified equations) combined with KAM theory. The book is illustrated by many figures, it treats applications from physics and astronomy and contains many numerical experiments and comparisons of different approaches. Note de contenu : - Examples and Numerical Experiments - Numerical Integrators - Order Conditions, Trees and B-Series - Conservation of First Integrals and Methods on Manifolds - Symmetric Integration and Reversibility - Symplectic Integration of Hamiltonian Systems - Further Topics in Structure Preservation - Structure-Preserving Implementation - Backward Error Analysis and Structure Preservation - Hamiltonian Perturbation Theory and Symplectic Integrators - Reversible Perturbation Theory and Symmetric Integrators - Dissipatively Perturbed Hamiltonian and Reversible Systems - Highly Oscillatory Differential Equations - Dynamics of Multistep Methods

Exemplaires

Code-barres	Cote	Support	Localisation	Section	Disponibilité	Etat_Exemplaire
046782	519.6 HAI	Papier	Bibliothèque Centrale	Mathématiques	Disponible