The Numerical Method Of Lines And Duality Principles Applied To Models In Physics And Engineering

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The Numerical Method of Lines and Duality Principles Applied to Models in Physics and Engineering

Author : Fabio Silva Botelho
Publisher : CRC Press
ISBN 13 : 1003848427
Total Pages : 328 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis The Numerical Method of Lines and Duality Principles Applied to Models in Physics and Engineering by : Fabio Silva Botelho

Download or read book The Numerical Method of Lines and Duality Principles Applied to Models in Physics and Engineering written by Fabio Silva Botelho and published by CRC Press. This book was released on 2024-02-06 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Numerical Method of Lines and Duality Principles Applied to Models in Physics and Engineering

Author : Fabio Silva Botelho
Publisher : CRC Press
ISBN 13 : 9781032192109
Total Pages : 0 pages
Book Rating : 4.1/5 (921 download)

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Book Synopsis The Numerical Method of Lines and Duality Principles Applied to Models in Physics and Engineering by : Fabio Silva Botelho

Functional Analysis, Calculus of Variations and Numerical Methods for Models in Physics and Engineering

Author : Fabio Silva Botelho
Publisher : CRC Press
ISBN 13 : 1000205878
Total Pages : 576 pages
Book Rating : 4.0/5 (2 download)

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Book Synopsis Functional Analysis, Calculus of Variations and Numerical Methods for Models in Physics and Engineering by : Fabio Silva Botelho

Download or read book Functional Analysis, Calculus of Variations and Numerical Methods for Models in Physics and Engineering written by Fabio Silva Botelho and published by CRC Press. This book was released on 2020-11-02 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Advanced Calculus and its Applications in Variational Quantum Mechanics and Relativity Theory

Author : Fabio Silva Botelho
Publisher : CRC Press
ISBN 13 : 1000411028
Total Pages : 335 pages
Book Rating : 4.0/5 (4 download)

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Book Synopsis Advanced Calculus and its Applications in Variational Quantum Mechanics and Relativity Theory by : Fabio Silva Botelho

Download or read book Advanced Calculus and its Applications in Variational Quantum Mechanics and Relativity Theory written by Fabio Silva Botelho and published by CRC Press. This book was released on 2021-07-12 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Functional Analysis, Calculus of Variations and Numerical Methods for Models in Physics and Engineering

Author : Fabio Silva Botelho
Publisher : CRC Press
ISBN 13 : 9780367510039
Total Pages : 588 pages
Book Rating : 4.5/5 (1 download)

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Book Synopsis Functional Analysis, Calculus of Variations and Numerical Methods for Models in Physics and Engineering by : Fabio Silva Botelho

Download or read book Functional Analysis, Calculus of Variations and Numerical Methods for Models in Physics and Engineering written by Fabio Silva Botelho and published by CRC Press. This book was released on 2022-05 with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Applied Mechanics Reviews

Author :
Publisher :
ISBN 13 :
Total Pages : 592 pages
Book Rating : 4.:/5 (26 download)

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Book Synopsis Applied Mechanics Reviews by :

Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1974 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Scientific and Technical Aerospace Reports

Author :
Publisher :
ISBN 13 :
Total Pages : 1036 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis Scientific and Technical Aerospace Reports by :

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1990 with total page 1036 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Fundamental Numerical Methods for Electrical Engineering

Author : Stanislaw Rosloniec
Publisher : Springer Science & Business Media
ISBN 13 : 3540795197
Total Pages : 294 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Fundamental Numerical Methods for Electrical Engineering by : Stanislaw Rosloniec

Download or read book Fundamental Numerical Methods for Electrical Engineering written by Stanislaw Rosloniec and published by Springer Science & Business Media. This book was released on 2008-07-17 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stormy development of electronic computation techniques (computer systems and software), observed during the last decades, has made possible automation of data processing in many important human activity areas, such as science, technology, economics and labor organization. In a broadly understood technology area, this developmentledtoseparationofspecializedformsofusingcomputersforthedesign and manufacturing processes, that is: – computer-aided design (CAD) – computer-aided manufacture (CAM) In order to show the role of computer in the rst of the two applications m- tioned above, let us consider basic stages of the design process for a standard piece of electronic system, or equipment: – formulation of requirements concerning user properties (characteristics, para- ters) of the designed equipment, – elaboration of the initial, possibly general electric structure, – determination of mathematical model of the system on the basis of the adopted electric structure, – determination of basic responses (frequency- or time-domain) of the system, on the base of previously established mathematical model, – repeated modi cation of the adopted diagram (changing its structure or element values) in case, when it does not satisfy the adopted requirements, – preparation of design and technological documentation, – manufacturing of model (prototype) series, according to the prepared docum- tation, – testing the prototype under the aspect of its electric properties, mechanical du- bility and sensitivity to environment conditions, – modi cation of prototype documentation, if necessary, and handing over the documentation to series production. The most important stages of the process under discussion are illustrated in Fig. I. 1. xi xii Introduction Fig. I.

Fundamentals of Engineering Numerical Analysis

Author : Parviz Moin
Publisher : Cambridge University Press
ISBN 13 : 1139489550
Total Pages : 257 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Fundamentals of Engineering Numerical Analysis by : Parviz Moin

Download or read book Fundamentals of Engineering Numerical Analysis written by Parviz Moin and published by Cambridge University Press. This book was released on 2010-08-23 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the original publication of this book, available computer power has increased greatly. Today, scientific computing is playing an ever more prominent role as a tool in scientific discovery and engineering analysis. In this second edition, the key addition is an introduction to the finite element method. This is a widely used technique for solving partial differential equations (PDEs) in complex domains. This text introduces numerical methods and shows how to develop, analyse, and use them. Complete MATLAB programs for all the worked examples are now available at www.cambridge.org/Moin, and more than 30 exercises have been added. This thorough and practical book is intended as a first course in numerical analysis, primarily for new graduate students in engineering and physical science. Along with mastering the fundamentals of numerical methods, students will learn to write their own computer programs using standard numerical methods.

Mathematical Methods for Physics and Engineering

Author : Kenneth Franklin Riley
Publisher :
ISBN 13 :
Total Pages : 1008 pages
Book Rating : 4.:/5 (641 download)

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Book Synopsis Mathematical Methods for Physics and Engineering by : Kenneth Franklin Riley

Download or read book Mathematical Methods for Physics and Engineering written by Kenneth Franklin Riley and published by . This book was released on 1997 with total page 1008 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Numerical Algorithms

Author : Justin Solomon
Publisher : CRC Press
ISBN 13 : 1482251892
Total Pages : 400 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Numerical Algorithms by : Justin Solomon

Download or read book Numerical Algorithms written by Justin Solomon and published by CRC Press. This book was released on 2015-06-24 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics presents a new approach to numerical analysis for modern computer scientists. Using examples from a broad base of computational tasks, including data processing, computational photography, and animation, the textbook introduces numerical modeling and algorithmic desig

Partial Differential Equations in Action

Author : Sandro Salsa
Publisher : Springer
ISBN 13 : 3319150936
Total Pages : 714 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Partial Differential Equations in Action by : Sandro Salsa

Download or read book Partial Differential Equations in Action written by Sandro Salsa and published by Springer. This book was released on 2015-04-24 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering. It has evolved from courses offered on partial differential equations (PDEs) over the last several years at the Politecnico di Milano. These courses had a twofold purpose: on the one hand, to teach students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other to provide them with a solid theoretical background in numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first part, chapters 2 to 5, is more elementary in nature and focuses on developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. In turn the second part, chapters 6 to 11, concentrates on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear boundary and initial-boundary value problems.

Undergraduate Announcement

Author : University of Michigan--Dearborn
Publisher :
ISBN 13 :
Total Pages : 220 pages
Book Rating : 4.3/5 (97 download)

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Book Synopsis Undergraduate Announcement by : University of Michigan--Dearborn

Download or read book Undergraduate Announcement written by University of Michigan--Dearborn and published by . This book was released on 1989 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Finite Difference Methods in Financial Engineering

Author : Daniel J. Duffy
Publisher : John Wiley & Sons
ISBN 13 : 1118856481
Total Pages : 452 pages
Book Rating : 4.1/5 (188 download)

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Book Synopsis Finite Difference Methods in Financial Engineering by : Daniel J. Duffy

Download or read book Finite Difference Methods in Financial Engineering written by Daniel J. Duffy and published by John Wiley & Sons. This book was released on 2013-10-28 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: The world of quantitative finance (QF) is one of the fastest growing areas of research and its practical applications to derivatives pricing problem. Since the discovery of the famous Black-Scholes equation in the 1970's we have seen a surge in the number of models for a wide range of products such as plain and exotic options, interest rate derivatives, real options and many others. Gone are the days when it was possible to price these derivatives analytically. For most problems we must resort to some kind of approximate method. In this book we employ partial differential equations (PDE) to describe a range of one-factor and multi-factor derivatives products such as plain European and American options, multi-asset options, Asian options, interest rate options and real options. PDE techniques allow us to create a framework for modeling complex and interesting derivatives products. Having defined the PDE problem we then approximate it using the Finite Difference Method (FDM). This method has been used for many application areas such as fluid dynamics, heat transfer, semiconductor simulation and astrophysics, to name just a few. In this book we apply the same techniques to pricing real-life derivative products. We use both traditional (or well-known) methods as well as a number of advanced schemes that are making their way into the QF literature: Crank-Nicolson, exponentially fitted and higher-order schemes for one-factor and multi-factor options Early exercise features and approximation using front-fixing, penalty and variational methods Modelling stochastic volatility models using Splitting methods Critique of ADI and Crank-Nicolson schemes; when they work and when they don't work Modelling jumps using Partial Integro Differential Equations (PIDE) Free and moving boundary value problems in QF Included with the book is a CD containing information on how to set up FDM algorithms, how to map these algorithms to C++ as well as several working programs for one-factor and two-factor models. We also provide source code so that you can customize the applications to suit your own needs.

Mathematical Reviews

Author :
Publisher :
ISBN 13 :
Total Pages : 1280 pages
Book Rating : 4.X/5 (6 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2003 with total page 1280 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to Numerical Geodynamic Modelling

Author : Taras Gerya
Publisher : Cambridge University Press
ISBN 13 : 0521887542
Total Pages : 359 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis Introduction to Numerical Geodynamic Modelling by : Taras Gerya

Download or read book Introduction to Numerical Geodynamic Modelling written by Taras Gerya and published by Cambridge University Press. This book was released on 2010 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: This user-friendly reference for students and researchers presents the basic mathematical theory, before introducing modelling of key geodynamic processes.

Analytic Methods for Partial Differential Equations

Author : G. Evans
Publisher : Springer Science & Business Media
ISBN 13 : 1447103793
Total Pages : 308 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Analytic Methods for Partial Differential Equations by : G. Evans

Download or read book Analytic Methods for Partial Differential Equations written by G. Evans and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the practical introduction to the analytical approach taken in Volume 2. Based upon courses in partial differential equations over the last two decades, the text covers the classic canonical equations, with the method of separation of variables introduced at an early stage. The characteristic method for first order equations acts as an introduction to the classification of second order quasi-linear problems by characteristics. Attention then moves to different co-ordinate systems, primarily those with cylindrical or spherical symmetry. Hence a discussion of special functions arises quite naturally, and in each case the major properties are derived. The next section deals with the use of integral transforms and extensive methods for inverting them, and concludes with links to the use of Fourier series.