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Título : Adaptive Moving Mesh Methods Tipo de documento: documento electrónico Autores: Huang, Weizhang ; SpringerLink (Online service) ; Russell, Robert D Editorial: New York, NY : Springer New York Fecha de publicación: 2011 Colección: Applied Mathematical Sciences, ISSN 0066-5452 num. 174 Número de páginas: XVIII, 434 p Il.: online resource ISBN/ISSN/DL: 978-1-4419-7916-2 Idioma : Inglés (eng) Palabras clave: Mathematics Partial differential equations Computer mathematics Numerical analysis Analysis Computational and Differential Equations Clasificación: 51 Matemáticas Resumen: Moving mesh methods are an effective, mesh-adaptation-based approach for the numerical solution of mathematical models of physical phenomena. Currently there exist three main strategies for mesh adaptation, namely, to use mesh subdivision, local high order approximation (sometimes combined with mesh subdivision), and mesh movement. The latter type of adaptive mesh method has been less well studied, both computationally and theoretically. This book is about adaptive mesh generation and moving mesh methods for the numerical solution of time-dependent partial differential equations. It presents a general framework and theory for adaptive mesh generation and gives a comprehensive treatment of moving mesh methods and their basic components, along with their application for a number of nontrivial physical problems. Many explicit examples with computed figures illustrate the various methods and the effects of parameter choices for those methods. The partial differential equations considered are mainly parabolic (diffusion-dominated, rather than convection-dominated). The extensive bibliography provides an invaluable guide to the literature in this field. Each chapter contains useful exercises. Graduate students, researchers and practitioners working in this area will benefit from this book. Weizhang Huang is a Professor in the Department of Mathematics at the University of Kansas. Robert D. Russell is a Professor in the Department of Mathematics at Simon Fraser University Nota de contenido: Preface -- Introduction -- Adaptive Mesh Movement in 1D -- Discretization of PDEs on Time-Varying Meshes -- Basic Principles of Multidimensional Mesh Adaption -- Monitor Functions -- Variational Mesh Adaptive Methods -- Velocity-Based Adaptive Methods -- Appendix: Sobolev Spaces -- Appendix: Arithmetic Mean Geometric Mean Inequality and Jensen's Inequality -- Bibliography En línea: http://dx.doi.org/10.1007/978-1-4419-7916-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33175 Adaptive Moving Mesh Methods [documento electrónico] / Huang, Weizhang ; SpringerLink (Online service) ; Russell, Robert D . - New York, NY : Springer New York, 2011 . - XVIII, 434 p : online resource. - (Applied Mathematical Sciences, ISSN 0066-5452; 174) .
ISBN : 978-1-4419-7916-2
Idioma : Inglés (eng)
Palabras clave: Mathematics Partial differential equations Computer mathematics Numerical analysis Analysis Computational and Differential Equations Clasificación: 51 Matemáticas Resumen: Moving mesh methods are an effective, mesh-adaptation-based approach for the numerical solution of mathematical models of physical phenomena. Currently there exist three main strategies for mesh adaptation, namely, to use mesh subdivision, local high order approximation (sometimes combined with mesh subdivision), and mesh movement. The latter type of adaptive mesh method has been less well studied, both computationally and theoretically. This book is about adaptive mesh generation and moving mesh methods for the numerical solution of time-dependent partial differential equations. It presents a general framework and theory for adaptive mesh generation and gives a comprehensive treatment of moving mesh methods and their basic components, along with their application for a number of nontrivial physical problems. Many explicit examples with computed figures illustrate the various methods and the effects of parameter choices for those methods. The partial differential equations considered are mainly parabolic (diffusion-dominated, rather than convection-dominated). The extensive bibliography provides an invaluable guide to the literature in this field. Each chapter contains useful exercises. Graduate students, researchers and practitioners working in this area will benefit from this book. Weizhang Huang is a Professor in the Department of Mathematics at the University of Kansas. Robert D. Russell is a Professor in the Department of Mathematics at Simon Fraser University Nota de contenido: Preface -- Introduction -- Adaptive Mesh Movement in 1D -- Discretization of PDEs on Time-Varying Meshes -- Basic Principles of Multidimensional Mesh Adaption -- Monitor Functions -- Variational Mesh Adaptive Methods -- Velocity-Based Adaptive Methods -- Appendix: Sobolev Spaces -- Appendix: Arithmetic Mean Geometric Mean Inequality and Jensen's Inequality -- Bibliography En línea: http://dx.doi.org/10.1007/978-1-4419-7916-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33175 Ejemplares
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Título : An Introduction to the Mathematical Theory of Inverse Problems Tipo de documento: documento electrónico Autores: Kirsch, Andreas ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2011 Otro editor: Imprint: Springer Colección: Applied Mathematical Sciences, ISSN 0066-5452 num. 120 Número de páginas: XIV, 310 p Il.: online resource ISBN/ISSN/DL: 978-1-4419-8474-6 Idioma : Inglés (eng) Palabras clave: Mathematics Differential equations Partial differential Applied mathematics Engineering Equations Ordinary Appl.Mathematics/Computational Methods of Clasificación: 51 Matemáticas Resumen: This book introduces the reader to the area of inverse problems. The study of inverse problems is of vital interest to many areas of science and technology such as geophysical exploration, system identification, nondestructive testing and ultrasonic tomography. The aim of this book is twofold: in the first part, the reader is exposed to the basic notions and difficulties encountered with ill-posed problems. Basic properties of regularization methods for linear ill-posed problems are studied by means of several simple analytical and numerical examples. The second part of the book presents three special nonlinear inverse problems in detail - the inverse spectral problem, the inverse problem of electrical impedance tomography (EIT), and the inverse scattering problem. The corresponding direct problems are studied with respect to existence, uniqueness and continuous dependence on parameters. Then some theoretical results as well as numerical procedures for the inverse problems are discussed. In this new edition, the Factorization Method is included as one of the prominent members in this monograph. Since the Factorization Method is particularly simple for the problem of EIT and this field has attracted a lot of attention during the past decade a chapter on EIT has been added in this monograph. The book is highly illustrated and contains many exercises. This together with the choice of material and its presentation in the book are new, thus making it particularly suitable for graduate students in mathematics and engineering Nota de contenido: Introduction and Basic Concepts -- Regularization Theory for Equations of the First Kind -- Regularization by Discretization -- Inverse Eigenvalue Problems -- An Inverse Problem in Electrical Impedance Tomography -- An Inverse Scattering Problem -- References -- Index En línea: http://dx.doi.org/10.1007/978-1-4419-8474-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33182 An Introduction to the Mathematical Theory of Inverse Problems [documento electrónico] / Kirsch, Andreas ; SpringerLink (Online service) . - New York, NY : Springer New York : Imprint: Springer, 2011 . - XIV, 310 p : online resource. - (Applied Mathematical Sciences, ISSN 0066-5452; 120) .
ISBN : 978-1-4419-8474-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Differential equations Partial differential Applied mathematics Engineering Equations Ordinary Appl.Mathematics/Computational Methods of Clasificación: 51 Matemáticas Resumen: This book introduces the reader to the area of inverse problems. The study of inverse problems is of vital interest to many areas of science and technology such as geophysical exploration, system identification, nondestructive testing and ultrasonic tomography. The aim of this book is twofold: in the first part, the reader is exposed to the basic notions and difficulties encountered with ill-posed problems. Basic properties of regularization methods for linear ill-posed problems are studied by means of several simple analytical and numerical examples. The second part of the book presents three special nonlinear inverse problems in detail - the inverse spectral problem, the inverse problem of electrical impedance tomography (EIT), and the inverse scattering problem. The corresponding direct problems are studied with respect to existence, uniqueness and continuous dependence on parameters. Then some theoretical results as well as numerical procedures for the inverse problems are discussed. In this new edition, the Factorization Method is included as one of the prominent members in this monograph. Since the Factorization Method is particularly simple for the problem of EIT and this field has attracted a lot of attention during the past decade a chapter on EIT has been added in this monograph. The book is highly illustrated and contains many exercises. This together with the choice of material and its presentation in the book are new, thus making it particularly suitable for graduate students in mathematics and engineering Nota de contenido: Introduction and Basic Concepts -- Regularization Theory for Equations of the First Kind -- Regularization by Discretization -- Inverse Eigenvalue Problems -- An Inverse Problem in Electrical Impedance Tomography -- An Inverse Scattering Problem -- References -- Index En línea: http://dx.doi.org/10.1007/978-1-4419-8474-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33182 Ejemplares
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Título : Applications of Symmetry Methods to Partial Differential Equations Tipo de documento: documento electrónico Autores: Bluman, George W ; SpringerLink (Online service) ; Cheviakov, Alexei F ; Stephen C. Anco Editorial: New York, NY : Springer New York Fecha de publicación: 2010 Colección: Applied Mathematical Sciences, ISSN 0066-5452 num. 168 Número de páginas: XVIII, 398 p Il.: online resource ISBN/ISSN/DL: 978-0-387-68028-6 Idioma : Inglés (eng) Palabras clave: Mathematics Topological groups Lie Mathematical analysis Analysis (Mathematics) Groups, Groups Clasificación: 51 Matemáticas Resumen: This is an accessible book on advanced symmetry methods for partial differential equations. Topics include conservation laws, local symmetries, higher-order symmetries, contact transformations, delete "adjoint symmetries," Noether’s theorem, local mappings, nonlocally related PDE systems, potential symmetries, nonlocal symmetries, nonlocal conservation laws, nonlocal mappings, and the nonclassical method. Graduate students and researchers in mathematics, physics, and engineering will find this book useful. This book is a sequel to Symmetry and Integration Methods for Differential Equations (2002) by George W. Bluman and Stephen C. Anco. The emphasis in the present book is on how to find systematically symmetries (local and nonlocal) and conservation laws (local and nonlocal) of a given PDE system and how to use systematically symmetries and conservation laws for related applications Nota de contenido: Local Transformations and Conservation Laws -- Construction of Mappings Relating Differential Equations -- Nonlocally Related PDE Systems -- Applications of Nonlocally Related PDE Systems -- Further Applications of Symmetry Methods: Miscellaneous Extensions En línea: http://dx.doi.org/10.1007/978-0-387-68028-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33494 Applications of Symmetry Methods to Partial Differential Equations [documento electrónico] / Bluman, George W ; SpringerLink (Online service) ; Cheviakov, Alexei F ; Stephen C. Anco . - New York, NY : Springer New York, 2010 . - XVIII, 398 p : online resource. - (Applied Mathematical Sciences, ISSN 0066-5452; 168) .
ISBN : 978-0-387-68028-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Topological groups Lie Mathematical analysis Analysis (Mathematics) Groups, Groups Clasificación: 51 Matemáticas Resumen: This is an accessible book on advanced symmetry methods for partial differential equations. Topics include conservation laws, local symmetries, higher-order symmetries, contact transformations, delete "adjoint symmetries," Noether’s theorem, local mappings, nonlocally related PDE systems, potential symmetries, nonlocal symmetries, nonlocal conservation laws, nonlocal mappings, and the nonclassical method. Graduate students and researchers in mathematics, physics, and engineering will find this book useful. This book is a sequel to Symmetry and Integration Methods for Differential Equations (2002) by George W. Bluman and Stephen C. Anco. The emphasis in the present book is on how to find systematically symmetries (local and nonlocal) and conservation laws (local and nonlocal) of a given PDE system and how to use systematically symmetries and conservation laws for related applications Nota de contenido: Local Transformations and Conservation Laws -- Construction of Mappings Relating Differential Equations -- Nonlocally Related PDE Systems -- Applications of Nonlocally Related PDE Systems -- Further Applications of Symmetry Methods: Miscellaneous Extensions En línea: http://dx.doi.org/10.1007/978-0-387-68028-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33494 Ejemplares
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Título : Attractors for infinite-dimensional non-autonomous dynamical systems Tipo de documento: documento electrónico Autores: Carvalho, Alexandre N ; SpringerLink (Online service) ; Langa, José A ; Robinson, James C Editorial: New York, NY : Springer New York Fecha de publicación: 2013 Otro editor: Imprint: Springer Colección: Applied Mathematical Sciences, ISSN 0066-5452 num. 182 Número de páginas: XXXVI, 412 p Il.: online resource ISBN/ISSN/DL: 978-1-4614-4581-4 Idioma : Inglés (eng) Palabras clave: Mathematics Dynamics Ergodic theory Partial differential equations Manifolds (Mathematics) Complex manifolds Differential Equations Dynamical Systems and Theory Cell Complexes (incl. Diff.Topology) Clasificación: 51 Matemáticas Resumen: This book treats the theory of pullback attractors for non-autonomous dynamical systems. While the emphasis is on infinite-dimensional systems, the results are also applied to a variety of finite-dimensional examples. The purpose of the book is to provide a summary of the current theory, starting with basic definitions and proceeding all the way to state-of-the-art results. As such it is intended as a primer for graduate students, and a reference for more established researchers in the field. The basic topics are existence results for pullback attractors, their continuity under perturbation, techniques for showing that their fibres are finite-dimensional, and structural results for pullback attractors for small non-autonomous perturbations of gradient systems (those with a Lyapunov function). The structural results stem from a dynamical characterisation of autonomous gradient systems, which shows in particular that such systems are stable under perturbation. Application of the structural results relies on the continuity of unstable manifolds under perturbation, which in turn is based on the robustness of exponential dichotomies: a self-contained development of these topics is given in full. After providing all the necessary theory the book treats a number of model problems in detail, demonstrating the wide applicability of the definitions and techniques introduced: these include a simple Lotka-Volterra ordinary differential equation, delay differential equations, the two-dimensional Navier-Stokes equations, general reaction-diffusion problems, a non-autonomous version of the Chafee-Infante problem, a comparison of attractors in problems with perturbations to the diffusion term, and a non-autonomous damped wave equation. Alexandre N. Carvalho is a Professor at the University of Sao Paulo, Brazil. José A. Langa is a Profesor Titular at the University of Seville, Spain. James C. Robinson is a Professor at the University of Warwick, UK Nota de contenido: The pullback attractor -- Existence results for pullback attractors -- Continuity of attractors -- Finite-dimensional attractors -- Gradient semigroups and their dynamical properties -- Semilinear Differential Equations -- Exponential dichotomies -- Hyperbolic solutions and their stable and unstable manifolds -- A non-autonomous competitive Lotka-Volterra system -- Delay differential equations.-The Navier–Stokes equations with non-autonomous forcing.- Applications to parabolic problems -- A non-autonomous Chafee–Infante equation -- Perturbation of diffusion and continuity of attractors with rate -- A non-autonomous damped wave equation -- References -- Index.- En línea: http://dx.doi.org/10.1007/978-1-4614-4581-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32225 Attractors for infinite-dimensional non-autonomous dynamical systems [documento electrónico] / Carvalho, Alexandre N ; SpringerLink (Online service) ; Langa, José A ; Robinson, James C . - New York, NY : Springer New York : Imprint: Springer, 2013 . - XXXVI, 412 p : online resource. - (Applied Mathematical Sciences, ISSN 0066-5452; 182) .
ISBN : 978-1-4614-4581-4
Idioma : Inglés (eng)
Palabras clave: Mathematics Dynamics Ergodic theory Partial differential equations Manifolds (Mathematics) Complex manifolds Differential Equations Dynamical Systems and Theory Cell Complexes (incl. Diff.Topology) Clasificación: 51 Matemáticas Resumen: This book treats the theory of pullback attractors for non-autonomous dynamical systems. While the emphasis is on infinite-dimensional systems, the results are also applied to a variety of finite-dimensional examples. The purpose of the book is to provide a summary of the current theory, starting with basic definitions and proceeding all the way to state-of-the-art results. As such it is intended as a primer for graduate students, and a reference for more established researchers in the field. The basic topics are existence results for pullback attractors, their continuity under perturbation, techniques for showing that their fibres are finite-dimensional, and structural results for pullback attractors for small non-autonomous perturbations of gradient systems (those with a Lyapunov function). The structural results stem from a dynamical characterisation of autonomous gradient systems, which shows in particular that such systems are stable under perturbation. Application of the structural results relies on the continuity of unstable manifolds under perturbation, which in turn is based on the robustness of exponential dichotomies: a self-contained development of these topics is given in full. After providing all the necessary theory the book treats a number of model problems in detail, demonstrating the wide applicability of the definitions and techniques introduced: these include a simple Lotka-Volterra ordinary differential equation, delay differential equations, the two-dimensional Navier-Stokes equations, general reaction-diffusion problems, a non-autonomous version of the Chafee-Infante problem, a comparison of attractors in problems with perturbations to the diffusion term, and a non-autonomous damped wave equation. Alexandre N. Carvalho is a Professor at the University of Sao Paulo, Brazil. José A. Langa is a Profesor Titular at the University of Seville, Spain. James C. Robinson is a Professor at the University of Warwick, UK Nota de contenido: The pullback attractor -- Existence results for pullback attractors -- Continuity of attractors -- Finite-dimensional attractors -- Gradient semigroups and their dynamical properties -- Semilinear Differential Equations -- Exponential dichotomies -- Hyperbolic solutions and their stable and unstable manifolds -- A non-autonomous competitive Lotka-Volterra system -- Delay differential equations.-The Navier–Stokes equations with non-autonomous forcing.- Applications to parabolic problems -- A non-autonomous Chafee–Infante equation -- Perturbation of diffusion and continuity of attractors with rate -- A non-autonomous damped wave equation -- References -- Index.- En línea: http://dx.doi.org/10.1007/978-1-4614-4581-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32225 Ejemplares
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Título : Averaging Methods in Nonlinear Dynamical Systems Tipo de documento: documento electrónico Autores: Sanders, Jan A ; SpringerLink (Online service) ; Verhulst, Ferdinand ; Murdock, James Editorial: New York, NY : Springer New York Fecha de publicación: 2007 Colección: Applied Mathematical Sciences, ISSN 0066-5452 num. 59 Número de páginas: XXIV, 434 p Il.: online resource ISBN/ISSN/DL: 978-0-387-48918-6 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Dynamics Ergodic theory Partial differential equations Physics Dynamical Systems and Theory Differential Equations Theoretical, Computational Clasificación: 51 Matemáticas Resumen: Perturbation theory and in particular normal form theory has shown strong growth during the last decades. So it is not surprising that the authors have presented an extensive revision of the first edition of the Averaging Methods in Nonlinear Dynamical Systems book. There are many changes, corrections and updates in chapters on Basic Material and Asymptotics, Averaging, and Attraction. Chapters on Periodic Averaging and Hyperbolicity, Classical (first level) Normal Form Theory, Nilpotent (classical) Normal Form, and Higher Level Normal Form Theory are entirely new and represent new insights in averaging, in particular its relation with dynamical systems and the theory of normal forms. Also new are surveys on invariant manifolds in Appendix C and averaging for PDEs in Appendix E. Since the first edition, the book has expanded in length and the third author, James Murdock has been added. Review of First Edition "One of the most striking features of the book is the nice collection of examples, which range from the very simple to some that are elaborate, realistic, and of considerable practical importance. Most of them are presented in careful detail and are illustrated with profuse, illuminating diagrams." - Mathematical Reviews Nota de contenido: Basic Material and Asymptotics -- Averaging: the Periodic Case -- Methodology of Averaging -- Averaging: the General Case -- Attraction -- Periodic Averaging and Hyperbolicity -- Averaging over Angles -- Passage Through Resonance -- From Averaging to Normal Forms -- Hamiltonian Normal Form Theory -- Classical (First-Level) Normal Form Theory -- Nilpotent (Classical) Normal Form -- Higher-Level Normal Form Theory -- The History of the Theory of Averaging -- A 4-Dimensional Example of Hopf Bifurcation -- Invariant Manifolds by Averaging -- Some Elementary Exercises in Celestial Mechanics -- On Averaging Methods for Partial Differential Equations En línea: http://dx.doi.org/10.1007/978-0-387-48918-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34482 Averaging Methods in Nonlinear Dynamical Systems [documento electrónico] / Sanders, Jan A ; SpringerLink (Online service) ; Verhulst, Ferdinand ; Murdock, James . - New York, NY : Springer New York, 2007 . - XXIV, 434 p : online resource. - (Applied Mathematical Sciences, ISSN 0066-5452; 59) .
ISBN : 978-0-387-48918-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Dynamics Ergodic theory Partial differential equations Physics Dynamical Systems and Theory Differential Equations Theoretical, Computational Clasificación: 51 Matemáticas Resumen: Perturbation theory and in particular normal form theory has shown strong growth during the last decades. So it is not surprising that the authors have presented an extensive revision of the first edition of the Averaging Methods in Nonlinear Dynamical Systems book. There are many changes, corrections and updates in chapters on Basic Material and Asymptotics, Averaging, and Attraction. Chapters on Periodic Averaging and Hyperbolicity, Classical (first level) Normal Form Theory, Nilpotent (classical) Normal Form, and Higher Level Normal Form Theory are entirely new and represent new insights in averaging, in particular its relation with dynamical systems and the theory of normal forms. Also new are surveys on invariant manifolds in Appendix C and averaging for PDEs in Appendix E. Since the first edition, the book has expanded in length and the third author, James Murdock has been added. Review of First Edition "One of the most striking features of the book is the nice collection of examples, which range from the very simple to some that are elaborate, realistic, and of considerable practical importance. Most of them are presented in careful detail and are illustrated with profuse, illuminating diagrams." - Mathematical Reviews Nota de contenido: Basic Material and Asymptotics -- Averaging: the Periodic Case -- Methodology of Averaging -- Averaging: the General Case -- Attraction -- Periodic Averaging and Hyperbolicity -- Averaging over Angles -- Passage Through Resonance -- From Averaging to Normal Forms -- Hamiltonian Normal Form Theory -- Classical (First-Level) Normal Form Theory -- Nilpotent (Classical) Normal Form -- Higher-Level Normal Form Theory -- The History of the Theory of Averaging -- A 4-Dimensional Example of Hopf Bifurcation -- Invariant Manifolds by Averaging -- Some Elementary Exercises in Celestial Mechanics -- On Averaging Methods for Partial Differential Equations En línea: http://dx.doi.org/10.1007/978-0-387-48918-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34482 Ejemplares
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