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Computational Interval Methods for Engineering Applications

Computational Interval Methods for Engineering Applications
A Book

by Snehashish Chakraverty,Nisha Rani Mahato

  • Publisher : Academic Press
  • Release : 2020-11-01
  • Pages : 220
  • ISBN : 0128178590
  • Language : En, Es, Fr & De
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Computational Interval Methods for Engineering Applications explains how to use classical and advanced interval arithmetic to solve differential equations for a wide range of scientific and engineering problems. In mathematical models where there are variables and parameters of uncertain value, interval methods can be used as an efficient tool for handling this uncertainty. In addition, it can produce rigorous enclosures of solutions of practical problems governed by mathematical equations. Other topics discussed in the book include linear differential equations in areas such as robotics, control theory, and structural dynamics, and in nonlinear oscillators, such as Duffing and Van der Pol. The chaotic behavior of the enclosure of oscillators is also covered, as are static and dynamic analysis of engineering problems using the interval system of linear equations and eigenvalue problems, thus making this a comprehensive resource. Explains how interval arithmetic can be used to solve problems in a range of engineering disciplines, including structural and control Gives unique, comprehensive coverage of traditional and innovative interval techniques, with examples addressing both linear and nonlinear differential equations Provides full mathematical details of the governing differential equations used to solve a wide range of problems

Computational Methods in Engineering and Science

Computational Methods in Engineering and Science
With Applications to Fluid Dynamics and Nuclear Systems

by Shoichiro Nakamura

  • Publisher : Unknown Publisher
  • Release : 1977
  • Pages : 457
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Scientific Computing, Validated Numerics, Interval Methods

Scientific Computing, Validated Numerics, Interval Methods
A Book

by Walter Krämer,Jürgen Wolff von Gudenberg

  • Publisher : Springer Science & Business Media
  • Release : 2013-04-17
  • Pages : 398
  • ISBN : 1475764847
  • Language : En, Es, Fr & De
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Scan 2000, the GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics and Interval 2000, the International Conference on Interval Methods in Science and Engineering were jointly held in Karlsruhe, September 19-22, 2000. The joint conference continued the series of 7 previous Scan-symposia under the joint sponsorship of GAMM and IMACS. These conferences have traditionally covered the numerical and algorithmic aspects of scientific computing, with a strong emphasis on validation and verification of computed results as well as on arithmetic, programming, and algorithmic tools for this purpose. The conference further continued the series of 4 former Interval conferences focusing on interval methods and their application in science and engineering. The objectives are to propagate current applications and research as well as to promote a greater understanding and increased awareness of the subject matters. The symposium was held in Karlsruhe the European cradle of interval arithmetic and self-validating numerics and attracted 193 researchers from 33 countries. 12 invited and 153 contributed talks were given. But not only the quantity was overwhelming we were deeply impressed by the emerging maturity of our discipline. There were many talks discussing a wide variety of serious applications stretching all parts of mathematical modelling. New efficient, publicly available or even commercial tools were proposed or presented, and also foundations of the theory of intervals and reliable computations were considerably strengthened.

Numerical Methods in Engineering with Python

Numerical Methods in Engineering with Python
A Book

by Jaan Kiusalaas

  • Publisher : Cambridge University Press
  • Release : 2005-07-25
  • Pages : 424
  • ISBN : 9780521852876
  • Language : En, Es, Fr & De
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Numerical Methods in Engineering with Python, a student text, and a reference for practicing engineers.

Numerical Methods in Engineering with MATLAB®

Numerical Methods in Engineering with MATLAB®
A Book

by Jaan Kiusalaas

  • Publisher : Cambridge University Press
  • Release : 2005-08
  • Pages : 426
  • ISBN : 9780521852883
  • Language : En, Es, Fr & De
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Numerical Methods in Engineering with MATLAB®, a student text, and a reference for practicing engineers.

Combining Interval, Probabilistic, and Other Types of Uncertainty in Engineering Applications

Combining Interval, Probabilistic, and Other Types of Uncertainty in Engineering Applications
A Book

by Andrew Pownuk,Vladik Kreinovich

  • Publisher : Springer
  • Release : 2018-05-03
  • Pages : 202
  • ISBN : 3319910264
  • Language : En, Es, Fr & De
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How can we solve engineering problems while taking into account data characterized by different types of measurement and estimation uncertainty: interval, probabilistic, fuzzy, etc.? This book provides a theoretical basis for arriving at such solutions, as well as case studies demonstrating how these theoretical ideas can be translated into practical applications in the geosciences, pavement engineering, etc. In all these developments, the authors’ objectives were to provide accurate estimates of the resulting uncertainty; to offer solutions that require reasonably short computation times; to offer content that is accessible for engineers; and to be sufficiently general - so that readers can use the book for many different problems. The authors also describe how to make decisions under different types of uncertainty. The book offers a valuable resource for all practical engineers interested in better ways of gauging uncertainty, for students eager to learn and apply the new techniques, and for researchers interested in processing heterogeneous uncertainty.

Complex Interval Arithmetic and Its Applications

Complex Interval Arithmetic and Its Applications
A Book

by Miodrag Petkovic,Miodrag Petković,Miodrag S. Petkovic,Ljiljana Petković

  • Publisher : John Wiley & Sons
  • Release : 1998
  • Pages : 284
  • ISBN : 9783527401345
  • Language : En, Es, Fr & De
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The aim of this book is to present formulas and methods developed using complex interval arithmetic. While most of numerical methods described in the literature deal with real intervals and real vectors, there is no systematic study of methods in complex interval arithmetic. The book fills this gap. Several main subjects are considered: outer estimates for the range of complex functions, especially complex centered forms, the best approximations of elementary complex functions by disks, iterative methods for the inclusion by polynomial zeros including their implementation on parallel computers, the analysis of numerical stability of iterative methods by using complex interval arithmetic and numerical computation of curvilinear integrals with error bounds. Mainly new methods are presented developed over the last years, including a lot of very recent results by the authors some of which have not been published before.

Applied Mechanics Reviews

Applied Mechanics Reviews
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 1982
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Numerical Methods for Engineers and Scientists

Numerical Methods for Engineers and Scientists
An Introduction with Applications Using MATLAB

by Amos Gilat,Vish Subramaniam

  • Publisher : John Wiley & Sons Incorporated
  • Release : 2008
  • Pages : 459
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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A clear and concise guide to numerical methods and their application Mastering numerical methods has never been easier than with Gilat/Subramaniam’s Numerical Methods For Engineers and Scientists: An Introduction with Applications Using MATLAB. Uniquely accessible and concise, this book takes an innovative approach that integrates the study of numerical methods with hands-on programming practice using the popular MATLAB environment to solve realistic problems in engineering and science. Ideal for both students and professionals who would like to become more adept at numerical methods, Numerical Methods For Engineers and Scientists familiarizes you with: The mathematical background and fundamentals of numerical methods Solving nonlinear equations Solving a system of linear equations Eigenvalues and Eigenvectors Function approximation, curve fitting, and interpolation Differentiation Integration First-order and higher-order ODEs Initial and boundary value problems Using MATLAB’s built-in functions as tools for solving problems, you will practice applying numerical methods for analysis of real-world problems. All the information is presented in manageable, step-by-step fashion, supported by a large number of annotated examples and end-of-chapter problems. Lucid, carefully structured, and flexibly designed to fulfill a wide range of academic and practical needs, this book will help you develop the skills in numerical methods that will serve you well as a practicing engineer.

NUMERICAL METHODS FOR SCIENTISTS AND ENGINEERS, FOURTH EDITION

NUMERICAL METHODS FOR SCIENTISTS AND ENGINEERS, FOURTH EDITION
A Book

by Rao, K. Sankara

  • Publisher : PHI Learning Pvt. Ltd.
  • Release : 2017-12-01
  • Pages : 440
  • ISBN : 8193593898
  • Language : En, Es, Fr & De
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With a clarity of approach, this easy-to-comprehend book gives an in-depth analysis of the topics under Numerical Methods, in a systematic manner. Primarily intended for the undergraduate and postgraduate students in many branches of engineering, physics, mathematics and all those pursuing Bachelors/Masters in computer applications. Besides students, those appearing for competitive examinations, research scholars and professionals engaged in numerical computation will also be benefited by this book. The fourth edition of this book has been updated by adding a current topic of interest on Finite Element Methods, which is a versatile method to solve numerically, several problems that arise in engineering design, claiming many advantages over the existing methods. Besides, it introduces the basics in computing, discusses various direct and iterative methods for solving algebraic and transcendental equations and a system of non-linear equations, linear system of equations, matrix inversion and computation of eigenvalues and eigenvectors of a matrix. It also provides a detailed discussion on Curve fitting, Interpolation, Numerical Differentiation and Integration besides explaining various single step and predictor–corrector methods for solving ordinary differential equations, finite difference methods for solving partial differential equations, and numerical methods for solving Boundary Value Problems. Fourier series approximation to a real continuous function is also presented. The text is augmented with a plethora of examples and solved problems along with well-illustrated figures for a practical understanding of the subject. Chapter-end exercises with answers and a detailed bibliography have also been provided. NEW TO THIS EDITION • Includes two new chapters on the basic concepts of the Finite Element Method and Coordinate Systems in Finite Element Methods with Applications in Heat Transfer and Structural Mechanics. • Provides more than 350 examples including numerous worked-out problems. • Gives detailed solutions and hints to problems under Exercises.

Fundamental Numerical Methods for Electrical Engineering

Fundamental Numerical Methods for Electrical Engineering
A Book

by Stanislaw Rosloniec

  • Publisher : Springer Science & Business Media
  • Release : 2008-07-17
  • Pages : 284
  • ISBN : 3540795197
  • Language : En, Es, Fr & De
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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.

Numerical Methods for Engineers and Scientists, Second Edition,

Numerical Methods for Engineers and Scientists, Second Edition,
A Book

by Joe D. Hoffman,Steven Frankel

  • Publisher : CRC Press
  • Release : 2001-05-31
  • Pages : 840
  • ISBN : 9780824704438
  • Language : En, Es, Fr & De
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Emphasizing the finite difference approach for solving differential equations, the second edition of Numerical Methods for Engineers and Scientists presents a methodology for systematically constructing individual computer programs. Providing easy access to accurate solutions to complex scientific and engineering problems, each chapter begins with objectives, a discussion of a representative application, and an outline of special features, summing up with a list of tasks students should be able to complete after reading the chapter- perfect for use as a study guide or for review. The AIAA Journal calls the book "...a good, solid instructional text on the basic tools of numerical analysis."

Interval Finite Element Method with MATLAB

Interval Finite Element Method with MATLAB
A Book

by Sukanta Nayak,Snehashish Chakraverty

  • Publisher : Academic Press
  • Release : 2018-02-05
  • Pages : 168
  • ISBN : 0128129743
  • Language : En, Es, Fr & De
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Interval Finite Element Method with MATLAB provides a thorough introduction to an effective way of investigating problems involving uncertainty using computational modeling. The well-known and versatile Finite Element Method (FEM) is combined with the concept of interval uncertainties to develop the Interval Finite Element Method (IFEM). An interval or stochastic environment in parameters and variables is used in place of crisp ones to make the governing equations interval, thereby allowing modeling of the problem. The concept of interval uncertainties is systematically explained. Several examples are explored with IFEM using MATLAB on topics like spring mass, bar, truss and frame. Provides a systematic approach to understanding the interval uncertainties caused by vague or imprecise data Describes the interval finite element method in detail Gives step-by-step instructions for how to use MATLAB code for IFEM Provides a range of examples of IFEM in use, with accompanying MATLAB codes

Numerical Methods for Chemical Engineering

Numerical Methods for Chemical Engineering
Applications in MATLAB

by Kenneth J Beers,Kenneth J. Beers

  • Publisher : Cambridge University Press
  • Release : 2007
  • Pages : 474
  • ISBN : 9780521859714
  • Language : En, Es, Fr & De
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Applications of numerical mathematics and scientific computing to chemical engineering.

Scientific and Technical Aerospace Reports

Scientific and Technical Aerospace Reports
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 1984
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Theories of Interval Arithmetic

Theories of Interval Arithmetic
Mathematical Foundations and Applications

by Hend Dawood

  • Publisher : LAP Lambert Academic Publishing
  • Release : 2011-10-07
  • Pages : 128
  • ISBN : 3846501549
  • Language : En, Es, Fr & De
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Scientists are, all the time, in a struggle with uncertainty which is always a threat to a trustworthy scientific knowledge. A very simple and natural idea, to defeat uncertainty, is that of enclosing uncertain measured values in real closed intervals. On the basis of this idea, interval arithmetic is constructed. The idea of calculating with intervals is not completely new in mathematics: the concept has been known since Archimedes, who used guaranteed lower and upper bounds to compute his constant Pi. Interval arithmetic is now a broad field in which rigorous mathematics is associated with scientific computing. This connection makes it possible to solve uncertainty problems that cannot be efficiently solved by floating-point arithmetic. Today, application areas of interval methods include electrical engineering, control theory, remote sensing, experimental and computational physics, chaotic systems, celestial mechanics, signal processing, computer graphics, robotics, and computer-assisted proofs. The purpose of this book is to be a concise but informative introduction to the theories of interval arithmetic as well as to some of their computational and scientific applications. Editorial Reviews "This new book by Hend Dawood is a fresh introduction to some of the basics of interval computation. It stops short of discussing the more complicated subdivision methods for converging to ranges of values, however it provides a bit of perspective about complex interval arithmetic, constraint intervals, and modal intervals, and it does go into the design of hardware operations for interval arithmetic, which is something still to be done by computer manufacturers." - Ramon E. Moore, (The Founder of Interval Computations) Professor Emeritus of Computer and Information Science, Department of Mathematics, The Ohio State University, Columbus, U.S.A. "A popular math-oriented introduction to interval computations and its applications. This short book contains an explanation of the need for interval computations, a brief history of interval computations, and main interval computation techniques. It also provides an impressive list of main practical applications of interval techniques." - Vladik Kreinovich, (International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems) Professor of Computer Science, University of Texas at El Paso, El Paso, Texas, U.S.A. "I am delighted to see one more Egyptian citizen re-entering the field of interval mathematics invented in this very country thousands years ago." - Marek W. Gutowski, Institute of Physics, Polish Academy of Sciences, Warszawa, Poland

Numerical Methods for Engineering Application

Numerical Methods for Engineering Application
A Book

by Joel H. Ferziger

  • Publisher : John Wiley & Sons Incorporated
  • Release : 1981-10-09
  • Pages : 270
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Presents the numerical methods used in the solution of many engineering problems, including interpolation, integration, and ordinary and partial differential equations. Many methods are reduced to FORTRAN programs, with concrete examples demonstrating their actual behavior.

Numerical Methods for Differential Equations

Numerical Methods for Differential Equations
A Computational Approach

by J.R. Dormand

  • Publisher : CRC Press
  • Release : 1996-02-21
  • Pages : 384
  • ISBN : 9780849394331
  • Language : En, Es, Fr & De
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With emphasis on modern techniques, Numerical Methods for Differential Equations: A Computational Approach covers the development and application of methods for the numerical solution of ordinary differential equations. Some of the methods are extended to cover partial differential equations. All techniques covered in the text are on a program disk included with the book, and are written in Fortran 90. These programs are ideal for students, researchers, and practitioners because they allow for straightforward application of the numerical methods described in the text. The code is easily modified to solve new systems of equations. Numerical Methods for Differential Equations: A Computational Approach also contains a reliable and inexpensive global error code for those interested in global error estimation. This is a valuable text for students, who will find the derivations of the numerical methods extremely helpful and the programs themselves easy to use. It is also an excellent reference and source of software for researchers and practitioners who need computer solutions to differential equations.

Computational Methods for Linear Integral Equations

Computational Methods for Linear Integral Equations
A Book

by Prem Kythe,Pratap Puri

  • Publisher : Springer Science & Business Media
  • Release : 2002-04-26
  • Pages : 508
  • ISBN : 9780817641924
  • Language : En, Es, Fr & De
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This book presents numerical methods and computational aspects for linear integral equations. Such equations occur in various areas of applied mathematics, physics, and engineering. The material covered in this book, though not exhaustive, offers useful techniques for solving a variety of problems. Historical information cover ing the nineteenth and twentieth centuries is available in fragments in Kantorovich and Krylov (1958), Anselone (1964), Mikhlin (1967), Lonseth (1977), Atkinson (1976), Baker (1978), Kondo (1991), and Brunner (1997). Integral equations are encountered in a variety of applications in many fields including continuum mechanics, potential theory, geophysics, electricity and mag netism, kinetic theory of gases, hereditary phenomena in physics and biology, renewal theory, quantum mechanics, radiation, optimization, optimal control sys tems, communication theory, mathematical economics, population genetics, queue ing theory, and medicine. Most of the boundary value problems involving differ ential equations can be converted into problems in integral equations, but there are certain problems which can be formulated only in terms of integral equations. A computational approach to the solution of integral equations is, therefore, an essential branch of scientific inquiry.

Statistical Theory with Engineering Applications. Statistical Tables and Formulas

Statistical Theory with Engineering Applications. Statistical Tables and Formulas
A Book

by Anders Hald

  • Publisher : Unknown Publisher
  • Release : 1952
  • Pages : 97
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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