The Numerical Method of Lines and Duality Principles Applied to Models in Physics and Engineering PDF Download
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Author: Fabio Silva Botelho
Publisher: CRC Press
ISBN: 9781032192109
Category : Differential equations, Partial
Languages : en
Pages : 0
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Book Description
Author: Fabio Silva Botelho
Publisher: CRC Press
ISBN: 9781032192109
Category : Differential equations, Partial
Languages : en
Pages : 0
Get Book Here
Book Description
Author: Fabio Silva Botelho
Publisher: CRC Press
ISBN: 1003848427
Category : Science
Languages : en
Pages : 328
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Book Description
The book includes theoretical and applied results of a generalization of the numerical method of lines. A Ginzburg-Landau type equation comprises the initial application, with detailed explanations about the establishment of the general line expressions. Approximate numerical procedures have been developed for a variety of equation types, including the related algorithms and software. The applications include the Ginzburg-Landau system in superconductivity, applications to the Navier-Stokes system in fluid mechanics and, among others, models in flight mechanics. In its second and final parts, the book develops duality principles and numerical results for other similar and related models. The book is meant for applied mathematicians, physicists and engineers interested in numerical methods and concerning duality theory. It is expected the text will serve as a valuable auxiliary project tool for some important engineering and physics fields of research.
Author: Fabio Silva Botelho
Publisher: CRC Press
ISBN: 9780367510039
Category : Calculus of variations
Languages : en
Pages : 588
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Book Description
The book discusses basic concepts of functional analysis, measure and integration theory, calculus of variations and duality and its applications to variational problems of non-convex nature, such as the Ginzburg-Landau system in superconductivity, shape optimization models, dual variational formulations for micro-magnetism and others. Numerical Methods for such and similar problems, such as models in flight mechanics and the Navier-Stokes system in fluid mechanics have been developed through the generalized method of lines, including their matrix finite dimensional approximations. It concludes with a review of recent research on Riemannian geometry applied to Quantum Mechanics and Relativity. The book will be of interest to applied mathematicians and graduate students in applied mathematics. Physicists, engineers and researchers in related fields will also find the book useful in providing a mathematical background applicable to their respective professional areas.
Author: Fabio Silva Botelho
Publisher: CRC Press
ISBN: 1000205878
Category : Mathematics
Languages : en
Pages : 576
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Book Description
The book discusses basic concepts of functional analysis, measure and integration theory, calculus of variations and duality and its applications to variational problems of non-convex nature, such as the Ginzburg-Landau system in superconductivity, shape optimization models, dual variational formulations for micro-magnetism and others. Numerical Methods for such and similar problems, such as models in flight mechanics and the Navier-Stokes system in fluid mechanics have been developed through the generalized method of lines, including their matrix finite dimensional approximations. It concludes with a review of recent research on Riemannian geometry applied to Quantum Mechanics and Relativity. The book will be of interest to applied mathematicians and graduate students in applied mathematics. Physicists, engineers and researchers in related fields will also find the book useful in providing a mathematical background applicable to their respective professional areas.
Author: Fabio Silva Botelho
Publisher: CRC Press
ISBN: 1000411028
Category : Mathematics
Languages : en
Pages : 335
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Book Description
Presents a rigorous study on manifolds in Rn. Develops in details important standard topics on advanced calculus, such as the differential forms in surfaces in Rn. Presents a proposal to connect classical and quantum mechanics. Presents variational formulations for relativistic mechanics through semi-Riemannian geometry and differential geometry. Develops a rigorous study on causal structures in space-time manifolds.
Author: John R. Hauser
Publisher: Springer Science & Business Media
ISBN: 1402099207
Category : Technology & Engineering
Languages : en
Pages : 1013
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Book Description
There are many books on the use of numerical methods for solving engineering problems and for modeling of engineering artifacts. In addition there are many styles of such presentations ranging from books with a major emphasis on theory to books with an emphasis on applications. The purpose of this book is hopefully to present a somewhat different approach to the use of numerical methods for - gineering applications. Engineering models are in general nonlinear models where the response of some appropriate engineering variable depends in a nonlinear manner on the - plication of some independent parameter. It is certainly true that for many types of engineering models it is sufficient to approximate the real physical world by some linear model. However, when engineering environments are pushed to - treme conditions, nonlinear effects are always encountered. It is also such - treme conditions that are of major importance in determining the reliability or failure limits of engineering systems. Hence it is essential than engineers have a toolbox of modeling techniques that can be used to model nonlinear engineering systems. Such a set of basic numerical methods is the topic of this book. For each subject area treated, nonlinear models are incorporated into the discussion from the very beginning and linear models are simply treated as special cases of more general nonlinear models. This is a basic and fundamental difference in this book from most books on numerical methods.
Author: Greenspan
Publisher: Academic Press
ISBN: 0080956165
Category : Computers
Languages : en
Pages : 325
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Book Description
Discrete Numerical Methods in Physics and Engineering
Author: Mario César Suárez Arriaga
Publisher: CRC Press
ISBN: 0203886224
Category : Technology & Engineering
Languages : en
Pages : 496
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Book Description
Mathematics is a universal language. Differential equations, mathematical modeling, numerical methods and computation form the underlying infrastructure of engineering and the sciences. In this context mathematical modeling is a very powerful tool for studying engineering problems, natural systems and human society. This interdisciplinary book cont
Author: Myron B. Allen
Publisher: Wiley-Interscience
ISBN:
Category : Mathematics
Languages : en
Pages : 440
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Book Description
An unified approach to numerical modeling, integrating aspects of continuum mechanics, differential equations, and numerical analysis. Explains how to formulate a mathematical description of the phenomena under consideration, devise techniques for solving the governing equations, then refine the model and interpret the results. Emphasizes physical applications and relates the three major classes of partial differential equations -- elliptic, parabolic, and hyperbolic -- to steady-state systems, dissipative systems, and nondissipative systems, respectively. Also examines some higher-order equations, nonlinear equations, and coupled systems of equations.
Author: Carmen Chicone
Publisher: Academic Press
ISBN: 0128041544
Category : Mathematics
Languages : en
Pages : 880
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Book Description
An Invitation to Applied Mathematics: Differential Equations, Modeling, and Computation introduces the reader to the methodology of modern applied mathematics in modeling, analysis, and scientific computing with emphasis on the use of ordinary and partial differential equations. Each topic is introduced with an attractive physical problem, where a mathematical model is constructed using physical and constitutive laws arising from the conservation of mass, conservation of momentum, or Maxwell's electrodynamics. Relevant mathematical analysis (which might employ vector calculus, Fourier series, nonlinear ODEs, bifurcation theory, perturbation theory, potential theory, control theory, or probability theory) or scientific computing (which might include Newton's method, the method of lines, finite differences, finite elements, finite volumes, boundary elements, projection methods, smoothed particle hydrodynamics, or Lagrangian methods) is developed in context and used to make physically significant predictions. The target audience is advanced undergraduates (who have at least a working knowledge of vector calculus and linear ordinary differential equations) or beginning graduate students. Readers will gain a solid and exciting introduction to modeling, mathematical analysis, and computation that provides the key ideas and skills needed to enter the wider world of modern applied mathematics. Presents an integrated wealth of modeling, analysis, and numerical methods in one volume Provides practical and comprehensible introductions to complex subjects, for example, conservation laws, CFD, SPH, BEM, and FEM Includes a rich set of applications, with more appealing problems and projects suggested
