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Título : Modellistica numerica per problemi differenziali Tipo de documento: documento electrónico Autores: Alfio Quarteroni ; SpringerLink (Online service) Editorial: Milano : Springer Milan Fecha de publicación: 2008 Otro editor: Imprint: Springer Colección: UNITEXT, ISSN 2038-5714 num. 2 Número de páginas: XV, 561 pagg Il.: online resource ISBN/ISSN/DL: 978-88-470-0842-7 Idioma : Italiano (ita) Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Applied mathematics Engineering Computer Numerical models Mathematics, general Modeling and Industrial Applications of Computational Clasificación: 51 Matemáticas Resumen: In questo testo si introducono i concetti di base per la modellistica numerica di problemi differenziali alle derivate parziali. Si considerano le classiche equazioni lineari ellittiche, paraboliche ed iperboliche, ma anche altre equazioni, quali quelle di diffusione e trasporto, di Navier-Stokes, e le leggi di conservazione, e si forniscono numerosi esempi fisici che stanno alla base di tali equazioni. Quindi si analizzano metodi di risoluzione numerica basati su elementi finiti, differenze finite, volumi finiti, metodi spettrali e metodi di decomposizione di domini. In particolare vengono discussi gli aspetti algoritmici e di implementazione al calcolatore e si forniscono diversi programmi di semplice utilizzo. Il testo non presuppone una approfondita conoscenza matematica delle equazioni alle derivate parziali: i concetti rigorosamente indispensabili al riguardo sono riportati nell'Appendice. Esso è pertanto adatto agli studenti dei corsi di laurea di indirizzo scientifico (Ingegneria, Matematica, Fisica, Scienze dell'Informazione) e consigliabile a ricercatori del mondo accademico ed extra-accademico che vogliano avvicinarsi a questo interessante ramo della matematica applicata Nota de contenido: Richiami sulle equazioni alle derivate parziali -- Equazioni di tipo ellittico -- Il metodo di Galerkin-elementi finiti per problemi ellittici -- I metodi spettrali -- Equazioni di diffusione-trasporto-reazione -- Equazioni paraboliche -- Differenze finite per equazioni iperboliche -- Elementi finiti e metodi spettrali per equazioni iperboliche -- Cenni a problemi iperbolici non lineari -- Le equazioni di Navier-Stokes -- Cenni di programmazione degli elementi finiti -- Generazione di griglie in 1D e 2D -- Il metodo dei volumi finiti -- Il metodo di decomposizione dei domini -- Introduzione al controllo ottimale per equazioni a derivate parziali En línea: http://dx.doi.org/10.1007/978-88-470-0842-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34442 Modellistica numerica per problemi differenziali [documento electrónico] / Alfio Quarteroni ; SpringerLink (Online service) . - Milano : Springer Milan : Imprint: Springer, 2008 . - XV, 561 pagg : online resource. - (UNITEXT, ISSN 2038-5714; 2) .
ISBN : 978-88-470-0842-7
Idioma : Italiano (ita)
Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Applied mathematics Engineering Computer Numerical models Mathematics, general Modeling and Industrial Applications of Computational Clasificación: 51 Matemáticas Resumen: In questo testo si introducono i concetti di base per la modellistica numerica di problemi differenziali alle derivate parziali. Si considerano le classiche equazioni lineari ellittiche, paraboliche ed iperboliche, ma anche altre equazioni, quali quelle di diffusione e trasporto, di Navier-Stokes, e le leggi di conservazione, e si forniscono numerosi esempi fisici che stanno alla base di tali equazioni. Quindi si analizzano metodi di risoluzione numerica basati su elementi finiti, differenze finite, volumi finiti, metodi spettrali e metodi di decomposizione di domini. In particolare vengono discussi gli aspetti algoritmici e di implementazione al calcolatore e si forniscono diversi programmi di semplice utilizzo. Il testo non presuppone una approfondita conoscenza matematica delle equazioni alle derivate parziali: i concetti rigorosamente indispensabili al riguardo sono riportati nell'Appendice. Esso è pertanto adatto agli studenti dei corsi di laurea di indirizzo scientifico (Ingegneria, Matematica, Fisica, Scienze dell'Informazione) e consigliabile a ricercatori del mondo accademico ed extra-accademico che vogliano avvicinarsi a questo interessante ramo della matematica applicata Nota de contenido: Richiami sulle equazioni alle derivate parziali -- Equazioni di tipo ellittico -- Il metodo di Galerkin-elementi finiti per problemi ellittici -- I metodi spettrali -- Equazioni di diffusione-trasporto-reazione -- Equazioni paraboliche -- Differenze finite per equazioni iperboliche -- Elementi finiti e metodi spettrali per equazioni iperboliche -- Cenni a problemi iperbolici non lineari -- Le equazioni di Navier-Stokes -- Cenni di programmazione degli elementi finiti -- Generazione di griglie in 1D e 2D -- Il metodo dei volumi finiti -- Il metodo di decomposizione dei domini -- Introduzione al controllo ottimale per equazioni a derivate parziali En línea: http://dx.doi.org/10.1007/978-88-470-0842-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34442 Ejemplares
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Título : Modellistica Numerica per Problemi Differenziali Tipo de documento: documento electrónico Autores: Alfio Quarteroni ; SpringerLink (Online service) Editorial: Milano : Springer Milan Fecha de publicación: 2012 Otro editor: Imprint: Springer Colección: Collana Unitext, La Matematica per il 3+2, ISSN 2038-5714 Número de páginas: XII, 627 pagg Il.: online resource ISBN/ISSN/DL: 978-88-470-2748-0 Idioma : Italiano (ita) Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Applied mathematics Engineering Computer Numerical models Mathematics, general Modeling and Industrial Applications of Computational Clasificación: 51 Matemáticas Resumen: In questo testo si introducono i concetti di base per la modellistica numerica di problemi differenziali alle derivate parziali. Si considerano le classiche equazioni lineari ellittiche, paraboliche ed iperboliche, ma anche altre equazioni, quali quelle di diffusione e trasporto, di Navier-Stokes e le leggi di conservazione; si forniscono inoltre numerosi esempi fisici che stanno alla base di tali equazioni. Quindi si analizzano metodi di risoluzione numerica basati su elementi finiti (continui e discontinui), differenze finite, volumi finiti, metodi spettrali (continui e discontinui), nonché strategie di approssimazione più avanzate basate sui metodi di decomposizione di domini o quelli di risoluzione di problemi di controllo ottimale. In particolare vengono discussi gli aspetti algoritmici e di implementazione al calcolatore e si forniscono diversi programmi di semplice utilizzo. Il testo non presuppone una approfondita conoscenza matematica delle equazioni alle derivate parziali: i concetti rigorosamente indispensabili al riguardo sono riportati nell'Appendice. Esso è pertanto adatto agli studenti dei corsi di laurea di indirizzo scientifico (Ingegneria, Matematica, Fisica, Scienze dell'Informazione) e consigliabile a ricercatori del mondo accademico ed extra-accademico che vogliano avvicinarsi a questo interessante ramo della matematica applicata e delle scienze computazionali Nota de contenido: Richiami sulle equazioni alle derivate parziali -- Richiami di analisi funzionale -- Equazioni di tipo ellittico -- Il metodo di Galerkin-elementi finiti per problemi ellittici -- Equazioni paraboliche -- Generazione di griglie in 1D e 2D -- Algoritmi di risoluzione di sistemi lineari -- Cenni di programmazione degli elementi finiti -- Il metodo dei volumi finiti -- I metodi spettrali -- Metodi con elementi discontinui -- Equazioni di diffusione-trasporto-reazione -- Differenze finite per equazioni iperboliche -- Elementi finiti e metodi spettrali per equazioni iperboliche -- Cenni a problemi iperbolici non lineari -- Le equazioni di Navier-Stokes -- Introduzione al controllo ottimale per equazioni a derivate parziali -- Il metodo di decomposizione dei domini En línea: http://dx.doi.org/10.1007/978-88-470-2748-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33050 Modellistica Numerica per Problemi Differenziali [documento electrónico] / Alfio Quarteroni ; SpringerLink (Online service) . - Milano : Springer Milan : Imprint: Springer, 2012 . - XII, 627 pagg : online resource. - (Collana Unitext, La Matematica per il 3+2, ISSN 2038-5714) .
ISBN : 978-88-470-2748-0
Idioma : Italiano (ita)
Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Applied mathematics Engineering Computer Numerical models Mathematics, general Modeling and Industrial Applications of Computational Clasificación: 51 Matemáticas Resumen: In questo testo si introducono i concetti di base per la modellistica numerica di problemi differenziali alle derivate parziali. Si considerano le classiche equazioni lineari ellittiche, paraboliche ed iperboliche, ma anche altre equazioni, quali quelle di diffusione e trasporto, di Navier-Stokes e le leggi di conservazione; si forniscono inoltre numerosi esempi fisici che stanno alla base di tali equazioni. Quindi si analizzano metodi di risoluzione numerica basati su elementi finiti (continui e discontinui), differenze finite, volumi finiti, metodi spettrali (continui e discontinui), nonché strategie di approssimazione più avanzate basate sui metodi di decomposizione di domini o quelli di risoluzione di problemi di controllo ottimale. In particolare vengono discussi gli aspetti algoritmici e di implementazione al calcolatore e si forniscono diversi programmi di semplice utilizzo. Il testo non presuppone una approfondita conoscenza matematica delle equazioni alle derivate parziali: i concetti rigorosamente indispensabili al riguardo sono riportati nell'Appendice. Esso è pertanto adatto agli studenti dei corsi di laurea di indirizzo scientifico (Ingegneria, Matematica, Fisica, Scienze dell'Informazione) e consigliabile a ricercatori del mondo accademico ed extra-accademico che vogliano avvicinarsi a questo interessante ramo della matematica applicata e delle scienze computazionali Nota de contenido: Richiami sulle equazioni alle derivate parziali -- Richiami di analisi funzionale -- Equazioni di tipo ellittico -- Il metodo di Galerkin-elementi finiti per problemi ellittici -- Equazioni paraboliche -- Generazione di griglie in 1D e 2D -- Algoritmi di risoluzione di sistemi lineari -- Cenni di programmazione degli elementi finiti -- Il metodo dei volumi finiti -- I metodi spettrali -- Metodi con elementi discontinui -- Equazioni di diffusione-trasporto-reazione -- Differenze finite per equazioni iperboliche -- Elementi finiti e metodi spettrali per equazioni iperboliche -- Cenni a problemi iperbolici non lineari -- Le equazioni di Navier-Stokes -- Introduzione al controllo ottimale per equazioni a derivate parziali -- Il metodo di decomposizione dei domini En línea: http://dx.doi.org/10.1007/978-88-470-2748-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33050 Ejemplares
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Título : Numerical Mathematics Tipo de documento: documento electrónico Autores: Alfio Quarteroni ; SpringerLink (Online service) ; Riccardo Sacco ; Fausto Saleri Editorial: New York, NY : Springer New York Fecha de publicación: 2007 Colección: Texts in Applied Mathematics, ISSN 0939-2475 num. 37 Número de páginas: XVIII, 657 p. 135 illus Il.: online resource ISBN/ISSN/DL: 978-3-540-49809-4 Idioma : Inglés (eng) Palabras clave: Mathematics Applied mathematics Engineering Numerical analysis Applications of Mathematics, general Analysis Appl.Mathematics/Computational Methods Clasificación: 51 Matemáticas Resumen: Numerical mathematics is the branch of mathematics that proposes, develops, analyzes and applies methods from scientific computing to several fields including analysis, linear algebra, geometry, approximation theory, functional equations, optimization and differential equations. Other disciplines, such as physics, the natural and biological sciences, engineering, and economics and the financial sciences frequently give rise to problems that need scientific computing for their solutions. As such, numerical mathematics is the crossroad of several disciplines of great relevance in modern applied sciences, and can become a crucial tool for their qualitative and quantitative analysis. One of the purposes of this book is to provide the mathematical foundations of numerical methods, to analyze their basic theoretical properties (stability, accuracy, computational complexity) and demonstrate their performance on examples and counterexamples which outline their pros and cons. This is done using the MATLABTM software environment which is user-friendly and widely adopted. Within any specific class of problems, the most appropriate scientific computing algorithms are reviewed, their theoretical analyses are carried out and the expected results are verified on a MATLABTM computer implementation. Every chapter is supplied with examples, exercises and applications of the discussed theory to the solution of real-life problems. This book is addressed to senior undergraduate and graduate students with particular focus on degree courses in engineering, mathematics, physics and computer sciences. The attention which is paid to the applications and the related development of software makes it valuable also for researchers and users of scientific computing in a large variety of professional fields. In this second edition, the readability of pictures, tables and program headings has been improved. Several changes in the chapters on iterative methods and on polynomial approximation have also been added. From the reviews of the first edition: "This is an excellent and modern textbook in numerical mathematics! It is primarily addressed to undergraduate students in mathematics, physics, computer science and engineering. But you will need a weekly 4 hour lecture for 3 terms lecture to teach all topics treated in this book! Well known methods as well as very new algorithms are given. The methods and their performances are demonstrated by illustrative examples and computer examples. Exercises shall help the reader to understand the theory and to apply it. MATLAB-software satisfies the need of user-friendliness. [....] In the reviewers opinion, the presented book is the best textbook in numerical mathematics edited in the last ten years." Zentralblatt für Mathematik 2001, 991.38387 Nota de contenido: Series Preface -- Preface -- I Getting Started -- 1. Foundations of Matrix Analysis -- 2 Principles of Numerical Mathematics -- II Numerical Linear Algebra -- 3 Direct Methods for the Solution of Linear Systems -- 4 Iterative Methods for Solving Linear Systems -- 5 Approximation of Eigenvalues and Eigenvectors -- III Around Functions and Functionals -- 6 Rootfinding for Nonlinear Equations -- 7 Nonlinear Systems and Numerical Optimization -- 8 Polynomial Interpolation -- 9 Numerical Integration -- IV Transforms, Differentiation and Problem Discretization -- 10 Orthogonal Polynomials in Approximation Theory -- 11 Numerical Solution of Ordinary Differential Equations -- 12 Two-Point Boundary Value Problems -- 13 Parabolic and Hyperbolic Initial Boundary Value Problems -- References -- Index of MATLAB Programs -- Index En línea: http://dx.doi.org/10.1007/b98885 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34644 Numerical Mathematics [documento electrónico] / Alfio Quarteroni ; SpringerLink (Online service) ; Riccardo Sacco ; Fausto Saleri . - New York, NY : Springer New York, 2007 . - XVIII, 657 p. 135 illus : online resource. - (Texts in Applied Mathematics, ISSN 0939-2475; 37) .
ISBN : 978-3-540-49809-4
Idioma : Inglés (eng)
Palabras clave: Mathematics Applied mathematics Engineering Numerical analysis Applications of Mathematics, general Analysis Appl.Mathematics/Computational Methods Clasificación: 51 Matemáticas Resumen: Numerical mathematics is the branch of mathematics that proposes, develops, analyzes and applies methods from scientific computing to several fields including analysis, linear algebra, geometry, approximation theory, functional equations, optimization and differential equations. Other disciplines, such as physics, the natural and biological sciences, engineering, and economics and the financial sciences frequently give rise to problems that need scientific computing for their solutions. As such, numerical mathematics is the crossroad of several disciplines of great relevance in modern applied sciences, and can become a crucial tool for their qualitative and quantitative analysis. One of the purposes of this book is to provide the mathematical foundations of numerical methods, to analyze their basic theoretical properties (stability, accuracy, computational complexity) and demonstrate their performance on examples and counterexamples which outline their pros and cons. This is done using the MATLABTM software environment which is user-friendly and widely adopted. Within any specific class of problems, the most appropriate scientific computing algorithms are reviewed, their theoretical analyses are carried out and the expected results are verified on a MATLABTM computer implementation. Every chapter is supplied with examples, exercises and applications of the discussed theory to the solution of real-life problems. This book is addressed to senior undergraduate and graduate students with particular focus on degree courses in engineering, mathematics, physics and computer sciences. The attention which is paid to the applications and the related development of software makes it valuable also for researchers and users of scientific computing in a large variety of professional fields. In this second edition, the readability of pictures, tables and program headings has been improved. Several changes in the chapters on iterative methods and on polynomial approximation have also been added. From the reviews of the first edition: "This is an excellent and modern textbook in numerical mathematics! It is primarily addressed to undergraduate students in mathematics, physics, computer science and engineering. But you will need a weekly 4 hour lecture for 3 terms lecture to teach all topics treated in this book! Well known methods as well as very new algorithms are given. The methods and their performances are demonstrated by illustrative examples and computer examples. Exercises shall help the reader to understand the theory and to apply it. MATLAB-software satisfies the need of user-friendliness. [....] In the reviewers opinion, the presented book is the best textbook in numerical mathematics edited in the last ten years." Zentralblatt für Mathematik 2001, 991.38387 Nota de contenido: Series Preface -- Preface -- I Getting Started -- 1. Foundations of Matrix Analysis -- 2 Principles of Numerical Mathematics -- II Numerical Linear Algebra -- 3 Direct Methods for the Solution of Linear Systems -- 4 Iterative Methods for Solving Linear Systems -- 5 Approximation of Eigenvalues and Eigenvectors -- III Around Functions and Functionals -- 6 Rootfinding for Nonlinear Equations -- 7 Nonlinear Systems and Numerical Optimization -- 8 Polynomial Interpolation -- 9 Numerical Integration -- IV Transforms, Differentiation and Problem Discretization -- 10 Orthogonal Polynomials in Approximation Theory -- 11 Numerical Solution of Ordinary Differential Equations -- 12 Two-Point Boundary Value Problems -- 13 Parabolic and Hyperbolic Initial Boundary Value Problems -- References -- Index of MATLAB Programs -- Index En línea: http://dx.doi.org/10.1007/b98885 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34644 Ejemplares
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Título : Numerical Mathematics Tipo de documento: documento electrónico Autores: Alfio Quarteroni ; Riccardo Sacco ; SpringerLink (Online service) ; Fausto Saleri Editorial: New York, NY : Springer New York Fecha de publicación: 2007 Otro editor: Imprint: Springer Colección: Texts in Applied Mathematics, ISSN 0939-2475 num. 37 Número de páginas: XX, 655 p. 126 illus Il.: online resource ISBN/ISSN/DL: 978-0-387-22750-4 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Applied mathematics Engineering Numerical Applications of Clasificación: 51 Matemáticas Resumen: Numerical mathematics is the branch of mathematics that proposes, develops, analyzes and applies methods from scientific computing to several fields including analysis, linear algebra, geometry, approximation theory, functional equations, optimization and differential equations. Other disciplines, such as physics, the natural and biological sciences, engineering, and economics and the financial sciences frequently give rise to problems that need scientific computing for their solutions. As such, numerical mathematics is the crossroad of several disciplines of great relevance in modern applied sciences, and can become a crucial tool for their qualitative and quantitative analysis. One of the purposes of this book is to provide the mathematical foundations of numerical methods, to analyze their basic theoretical properties (stability, accuracy, computational complexity) and demonstrate their performances on examples and counterexamples which outline their pros and cons. This is done using the MATLAB software environment which is user-friendly and widely adopted. Within any specific class of problems, the most appropriate scientific computing algorithms are reviewed, their theoretical analyses are carried out and the expected results are verified on a MATLAB computer implementation. Every chapter is supplied with examples, exercises and applications of the discussed theory to the solution of real-life problems. This book is addressed to senior undergraduate and graduate students with particular focus on degree courses in Engineering, Mathematics, Physics and Computer Sciences. The attention which is paid to the applications and the related development of software makes it valuable also for researchers and users of scientific computing in a large variety of professional fields Nota de contenido: Getting Started -- Foundations of Matrix Analysis -- Principles of Numerical Mathematics -- Numerical Linear Algebra -- Direct Methods for the Solution of Linear Systems -- Iterative Methods for Solving Linear Systems -- Approximation of Eigenvalues and Eigenvectors -- Around Functions and Functionals -- Rootfinding for Nonlinear Equations -- Nonlinear Systems and Numerical Optimization -- Polynomial Interpolation -- Numerical Integration -- Transforms, Differentiation and Problem Discretization -- Orthogonal Polynomials in Approximation Theory -- Numerical Solution of Ordinary Differential Equations -- Two-Point Boundary Value Problems -- Parabolic and Hyperbolic Initial Boundary Value Problems En línea: http://dx.doi.org/10.1007/b98885 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=42257 Numerical Mathematics [documento electrónico] / Alfio Quarteroni ; Riccardo Sacco ; SpringerLink (Online service) ; Fausto Saleri . - New York, NY : Springer New York : Imprint: Springer, 2007 . - XX, 655 p. 126 illus : online resource. - (Texts in Applied Mathematics, ISSN 0939-2475; 37) .
ISBN : 978-0-387-22750-4
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Applied mathematics Engineering Numerical Applications of Clasificación: 51 Matemáticas Resumen: Numerical mathematics is the branch of mathematics that proposes, develops, analyzes and applies methods from scientific computing to several fields including analysis, linear algebra, geometry, approximation theory, functional equations, optimization and differential equations. Other disciplines, such as physics, the natural and biological sciences, engineering, and economics and the financial sciences frequently give rise to problems that need scientific computing for their solutions. As such, numerical mathematics is the crossroad of several disciplines of great relevance in modern applied sciences, and can become a crucial tool for their qualitative and quantitative analysis. One of the purposes of this book is to provide the mathematical foundations of numerical methods, to analyze their basic theoretical properties (stability, accuracy, computational complexity) and demonstrate their performances on examples and counterexamples which outline their pros and cons. This is done using the MATLAB software environment which is user-friendly and widely adopted. Within any specific class of problems, the most appropriate scientific computing algorithms are reviewed, their theoretical analyses are carried out and the expected results are verified on a MATLAB computer implementation. Every chapter is supplied with examples, exercises and applications of the discussed theory to the solution of real-life problems. This book is addressed to senior undergraduate and graduate students with particular focus on degree courses in Engineering, Mathematics, Physics and Computer Sciences. The attention which is paid to the applications and the related development of software makes it valuable also for researchers and users of scientific computing in a large variety of professional fields Nota de contenido: Getting Started -- Foundations of Matrix Analysis -- Principles of Numerical Mathematics -- Numerical Linear Algebra -- Direct Methods for the Solution of Linear Systems -- Iterative Methods for Solving Linear Systems -- Approximation of Eigenvalues and Eigenvectors -- Around Functions and Functionals -- Rootfinding for Nonlinear Equations -- Nonlinear Systems and Numerical Optimization -- Polynomial Interpolation -- Numerical Integration -- Transforms, Differentiation and Problem Discretization -- Orthogonal Polynomials in Approximation Theory -- Numerical Solution of Ordinary Differential Equations -- Two-Point Boundary Value Problems -- Parabolic and Hyperbolic Initial Boundary Value Problems En línea: http://dx.doi.org/10.1007/b98885 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=42257 Ejemplares
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Título : Numerical Models for Differential Problems Tipo de documento: documento electrónico Autores: Alfio Quarteroni ; SpringerLink (Online service) Editorial: Milano : Springer Milan Fecha de publicación: 2009 Colección: MS&A, ISSN 2037-5255 num. 2 Número de páginas: XVI, 601 p Il.: online resource ISBN/ISSN/DL: 978-88-470-1071-0 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Applied mathematics Engineering Computer Numerical models Mathematics, general Modeling and Industrial Applications of Computational Clasificación: 51 Matemáticas Resumen: In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. We then analyze numerical solution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods, and reduced basis methods. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, and recommendable to those researchers in the academic and extra-academic domain who want to approach this interesting branch of applied mathematics Nota de contenido: A brief survey on partial differential equations -- Elements of functional analysis -- Elliptic equations -- The Galerkin finite element method for elliptic problems -- Parabolic equations -- Generation of 1D and 2D grids -- Algorithms for the solution of linear systems -- Elements of finite element programming -- The finite volume method -- Spectral methods -- Diffusion-transport-reaction equations -- Finite differences for hyperbolic equations -- Finite elements and spectral methods for hyperbolic equations -- Nonlinear hyperbolic problems -- Navier-Stokes equations -- Optimal control of partial differential equations -- Domain decomposition methods -- Reduced basis approximation for parametrized partial differential equations En línea: http://dx.doi.org/10.1007/978-88-470-1071-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34123 Numerical Models for Differential Problems [documento electrónico] / Alfio Quarteroni ; SpringerLink (Online service) . - Milano : Springer Milan, 2009 . - XVI, 601 p : online resource. - (MS&A, ISSN 2037-5255; 2) .
ISBN : 978-88-470-1071-0
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Applied mathematics Engineering Computer Numerical models Mathematics, general Modeling and Industrial Applications of Computational Clasificación: 51 Matemáticas Resumen: In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. We then analyze numerical solution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods, and reduced basis methods. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, and recommendable to those researchers in the academic and extra-academic domain who want to approach this interesting branch of applied mathematics Nota de contenido: A brief survey on partial differential equations -- Elements of functional analysis -- Elliptic equations -- The Galerkin finite element method for elliptic problems -- Parabolic equations -- Generation of 1D and 2D grids -- Algorithms for the solution of linear systems -- Elements of finite element programming -- The finite volume method -- Spectral methods -- Diffusion-transport-reaction equations -- Finite differences for hyperbolic equations -- Finite elements and spectral methods for hyperbolic equations -- Nonlinear hyperbolic problems -- Navier-Stokes equations -- Optimal control of partial differential equations -- Domain decomposition methods -- Reduced basis approximation for parametrized partial differential equations En línea: http://dx.doi.org/10.1007/978-88-470-1071-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34123 Ejemplares
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