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Sinopsis
IN THIS TEXT, WE INTRODUCE THE BASIC CONCEPTS FOR THE NUMERICAL MODELING 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.<DIV><BR/></DIV>
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Reseña del editor
In this text, we introduce the basic concepts for the numerical modeling 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.
Biografía del autor
The Author is Professor and Director of the Chair of Modelling and Scientific Computing (CMCS) at the Institute of Analysis and Scientific Computing of EPFL, Lausanne (Switzerland), since 1998, Professor of Numerical Analysis at the Politecnico di Milano (Italy) since 1989, and Scientific Director of MOX, since 2002. Author of 22 books published with Springer, and of about 200 papers published in refereed international Journals, Conference Proceedings and Magazines, Alfio Quarteroni is actually one of the strongest and reliable mathematicians in the world in the field of Modelling and SC.
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- EditorialSpringer
- Año de publicación2017
- ISBN 10 3319493159
- ISBN 13 9783319493152
- EncuadernaciónTapa dura
- IdiomaInglés
- Número de edición3
- Número de páginas714
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Numerical Models for Differential Problems (MS&A, 16)
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Numerical Models for Differential Problems (MS&A, 16)
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Numerical Models for Differential Problems
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Buch. Condición: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -In this text, we introduce the basic concepts for the numerical modeling 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. 712 pp. Englisch. Nº de ref. del artículo: 9783319493152
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Numerical Models for Differential Problems (MS&A, 16)
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Numerical Models for Differential Problems
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ISBN 10: 3319493159
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Buch. Condición: Neu. Druck auf Anfrage Neuware - Printed after ordering - In this text, we introduce the basic concepts for the numerical modeling 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. Nº de ref. del artículo: 9783319493152
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