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Computational Interval Methods for Engineering Applications

Computational Interval Methods for Engineering Applications
  • Author : Snehashish Chakraverty,Nisha Rani Mahato
  • Publisher :Unknown
  • Release Date :2020-11-01
  • Total pages :220
  • ISBN : 9780128178591
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Summary : 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

Computational Methods in Engineering
  • Author : S.P. Venkateshan,Prasanna Swaminathan
  • Publisher :Unknown
  • Release Date :2013-12-09
  • Total pages :692
  • ISBN : 9780124167032
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Summary : Computational Methods in Engineering brings to light the numerous uses of numerical methods in engineering. It clearly explains the application of these methods mathematically and practically, emphasizing programming aspects when appropriate. By approaching the cross-disciplinary topic of numerical methods with a flexible approach, Computational Methods in Engineering encourages a well-rounded understanding of the subject. This book's teaching goes beyond the text—detailed exercises (with solutions), real examples of numerical methods in real engineering practices, flowcharts, and MATLAB codes all help you learn the methods directly in the medium that suits you best. Balanced discussion of mathematical principles and engineering applications Detailed step-by-step exercises and practical engineering examples to help engineering students and other readers fully grasp the concepts Concepts are explained through flowcharts and simple MATLAB codes to help you develop additional programming skills

Numerical Methods for Engineering Applications

Numerical Methods for Engineering Applications
  • Author : Joel H. Ferziger
  • Publisher :Unknown
  • Release Date :1998-04-17
  • Total pages :378
  • ISBN : STANFORD:36105020141540
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Summary : State-of-the-art numerical methods for solving complex engineering problems Great strides in computer technology have been made in the years since the popular first edition of this book was published. Several excellent software packages now help engineers solve complex problems. Making the most of these programs requires a working knowledge of the numerical methods on which the programs are based. Numerical Methods for Engineering Application provides that knowledge. While it avoids intense mathematical detail, Numerical Methods for Engineering Application supplies more in-depth explanations of methods than found in the typical engineer's numerical "cookbook." It offers complete coverage of most commonly encountered algebraic, interpolation, and integration problems. Ordinary differential equations are examined in great detail, as are three common types of partial differential equations--parabolic, elliptic, and hyperbolic. The author also explores a wide range of methods for solving initial and boundary value problems. This complete guide to numerical methods for solving engineering problems on computers provides: * Practical advice on how to select the best method for a given problem * Valuable insights into how each method works and why it is the best choice * Complete algorithms and source code for all programs covered * Code from the book and problem-solving programs designed by the author available from the author's website Numerical Methods for Engineering Application is a valuable working resource for engineers and applied physicists. It also serves as an excellent upper-level text for physics and engineering students in courses on modern numerical methods.

Scientific Computing, Validated Numerics, Interval Methods

Scientific Computing, Validated Numerics, Interval Methods
  • Author : Walter Krämer,Jürgen Wolff von Gudenberg
  • Publisher :Unknown
  • Release Date :2013-04-17
  • Total pages :398
  • ISBN : 9781475764840
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Summary : 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.

Computational Methods in Engineering and Science

Computational Methods in Engineering and Science
  • Author : Shoichiro Nakamura
  • Publisher :Unknown
  • Release Date :1977
  • Total pages :457
  • ISBN : UCSD:31822011719523
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Summary :

Computational Complexity and Feasibility of Data Processing and Interval Computations

Computational Complexity and Feasibility of Data Processing and Interval Computations
  • Author : V. Kreinovich,A.V. Lakeyev,J. Rohn,P.T. Kahl
  • Publisher :Unknown
  • Release Date :2013-06-29
  • Total pages :459
  • ISBN : 9781475727937
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Summary : Targeted audience • Specialists in numerical computations, especially in numerical optimiza tion, who are interested in designing algorithms with automatie result ver ification, and who would therefore be interested in knowing how general their algorithms caIi in principle be. • Mathematicians and computer scientists who are interested in the theory 0/ computing and computational complexity, especially computational com plexity of numerical computations. • Students in applied mathematics and computer science who are interested in computational complexity of different numerical methods and in learning general techniques for estimating this computational complexity. The book is written with all explanations and definitions added, so that it can be used as a graduate level textbook. What this book .is about Data processing. In many real-life situations, we are interested in the value of a physical quantity y that is diflicult (or even impossible) to measure directly. For example, it is impossible to directly measure the amount of oil in an oil field or a distance to a star. Since we cannot measure such quantities directly, we measure them indirectly, by measuring some other quantities Xi and using the known relation between y and Xi'S to reconstruct y. The algorithm that transforms the results Xi of measuring Xi into an estimate fj for y is called data processing.

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

Combining Interval, Probabilistic, and Other Types of Uncertainty in Engineering Applications
  • Author : Andrew Pownuk,Vladik Kreinovich
  • Publisher :Unknown
  • Release Date :2018-05-03
  • Total pages :202
  • ISBN : 9783319910260
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Summary : 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.

Wavelet Numerical Method and Its Applications in Nonlinear Problems

Wavelet Numerical Method and Its Applications in Nonlinear Problems
  • Author : You-He Zhou
  • Publisher :Unknown
  • Release Date :2021
  • Total pages :229
  • ISBN : 9789813366435
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Summary :

The Finite Element Method

The Finite Element Method
  • Author : Zhangxin Chen
  • Publisher :Unknown
  • Release Date :2011-10-06
  • Total pages :348
  • ISBN : 9789813100657
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Summary : This Finite Element Method offers a fundamental and practical introduction to the finite element method, its variants, and their applications in engineering. Every concept is introduced in the simplest possible setting, while maintaining a level of treatment that is as rigorous as possible without being unnecessarily abstract. Various finite elements in one, two, and three space dimensions are introduced, and their applications to elliptic, parabolic, hyperbolic, and nonlinear equations and to solid mechanics, fluid mechanics, and porous media flow problems are addressed. The variants include the control volume, multipoint flux approximation, nonconforming, mixed, discontinuous, characteristic, adaptive, and multiscale finite element methods. Illustrative computer programs in Fortran and C++ are described. An extensive set of exercises are provided in each chapter. This book serves as a text a for one-semester course for upper-level undergraduates and beginning graduate students and as a professional reference for engineers, mathematicians, and scientists.

Numerical Analysis with Applications in Mechanics and Engineering

Numerical Analysis with Applications in Mechanics and Engineering
  • Author : Petre Teodorescu,Nicolae-Doru Stanescu,Nicolae Pandrea
  • Publisher :Unknown
  • Release Date :2013-05-07
  • Total pages :646
  • ISBN : 9781118614624
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Summary : A much-needed guide on how to use numerical methods to solve practical engineering problems Bridging the gap between mathematics and engineering, Numerical Analysis with Applications in Mechanics and Engineering arms readers with powerful tools for solving real-world problems in mechanics, physics, and civil and mechanical engineering. Unlike most books on numerical analysis, this outstanding work links theory and application, explains the mathematics in simple engineering terms, and clearly demonstrates how to use numerical methods to obtain solutions and interpret results. Each chapter is devoted to a unique analytical methodology, including a detailed theoretical presentation and emphasis on practical computation. Ample numerical examples and applications round out the discussion, illustrating how to work out specific problems of mechanics, physics, or engineering. Readers will learn the core purpose of each technique, develop hands-on problem-solving skills, and get a complete picture of the studied phenomenon. Coverage includes: How to deal with errors in numerical analysis Approaches for solving problems in linear and nonlinear systems Methods of interpolation and approximation of functions Formulas and calculations for numerical differentiation and integration Integration of ordinary and partial differential equations Optimization methods and solutions for programming problems Numerical Analysis with Applications in Mechanics and Engineering is a one-of-a-kind guide for engineers using mathematical models and methods, as well as for physicists and mathematicians interested in engineering problems.

Computational Intelligence for Multimedia Big Data on the Cloud with Engineering Applications

Computational Intelligence for Multimedia Big Data on the Cloud with Engineering Applications
  • Author : Arun Kumar Sangaiah,Zhiyong Zhang,Michael Sheng
  • Publisher :Unknown
  • Release Date :2018-08-21
  • Total pages :362
  • ISBN : 9780128133279
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Summary : Computational Intelligence for Multimedia Big Data on the Cloud with Engineering Applications covers timely topics, including the neural network (NN), particle swarm optimization (PSO), evolutionary algorithm (GA), fuzzy sets (FS) and rough sets (RS), etc. Furthermore, the book highlights recent research on representative techniques to elaborate how a data-centric system formed a powerful platform for the processing of cloud hosted multimedia big data and how it could be analyzed, processed and characterized by CI. The book also provides a view on how techniques in CI can offer solutions in modeling, relationship pattern recognition, clustering and other problems in bioengineering. It is written for domain experts and developers who want to understand and explore the application of computational intelligence aspects (opportunities and challenges) for design and development of a data-centric system in the context of multimedia cloud, big data era and its related applications, such as smarter healthcare, homeland security, traffic control trading analysis and telecom, etc. Researchers and PhD students exploring the significance of data centric systems in the next paradigm of computing will find this book extremely useful. Presents a brief overview of computational intelligence paradigms and its significant role in application domains Illustrates the state-of-the-art and recent developments in the new theories and applications of CI approaches Familiarizes the reader with computational intelligence concepts and technologies that are successfully used in the implementation of cloud-centric multimedia services in massive data processing Provides new advances in the fields of CI for bio-engineering application

MATLAB Numerical Methods with Chemical Engineering Applications

MATLAB Numerical Methods with Chemical Engineering Applications
  • Author : Kamal Al-Malah
  • Publisher :Unknown
  • Release Date :2013-07-31
  • Total pages :384
  • ISBN : 9780071831291
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Summary : A practical, professional guide to MATLAB computational techniques and engineering applications MATLAB Numerical Methods with Chemical Engineering Applications shows you, step by step, how to use MATLAB® to model and simulate physical problems in the chemical engineering realm. Written for MATLAB 7.11, this hands-on resource contains concise explanations of essential MATLAB commands, as well as easy-to-follow instructions for using the programming features, graphical capabilities, and desktop interface. Every step needed toward the final solution is algorithmically explained via snapshots of the MATLAB platform in parallel with the text. End-of-chapter problems help you practice what you've learned. Master this powerful computational tool using this detailed, self-teaching guide. COVERAGE INCLUDES: MATLAB basics Matrices MATLAB scripting language: M-file Image and image analysis Curve-fitting Numerical integration Solving differential equations A system of algebraic equations Statistics Chemical engineering applications MATLAB Graphical User Interface Design Environment (GUIDE)

New Paradigms in Computational Modeling and Its Applications

New Paradigms in Computational Modeling and Its Applications
  • Author : Snehashish Chakraverty
  • Publisher :Unknown
  • Release Date :2021-01-25
  • Total pages :278
  • ISBN : 9780128221686
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Summary : In general, every problem of science and engineering is governed by mathematical models. There is often a need to model, solve and interpret the problems one encounters in the world of practical problems. Models of practical application problems usually need to be handled by efficient computational models. New Paradigms in Computational Modeling and Its Applications deals with recent developments in mathematical methods, including theoretical models as well as applied science and engineering. The book focuses on subjects that can benefit from mathematical methods with concepts of simulation, waves, dynamics, uncertainty, machine intelligence, and applied mathematics. The authors bring together leading-edge research on mathematics combining various fields of science and engineering. This perspective acknowledges the inherent characteristic of current research on mathematics operating in parallel over different subject fields. New Paradigms in Computational Modeling and Its Applications meets the present and future needs for the interaction between various science and technology/engineering areas on the one hand and different branches of mathematics on the other. As such, the book contains 13 chapters covering various aspects of computational modeling from theoretical to application problems. The first six chapters address various problems of structural and fluid dynamics. The next four chapters include solving problems where the governing parameters are uncertain regarding fuzzy, interval, and affine. The final three chapters will be devoted to the use of machine intelligence in artificial neural networks. Presents a self-contained and up to date review of modelling real life scientific and engineering application problems Introduces new concepts of various computing techniques to handle different engineering and science problems Demonstrates the efficiency and power of the various algorithms and models in a simple and easy to follow style, including numerous examples to illustrate concepts and algorithms

Interval Finite Element Method with MATLAB

Interval Finite Element Method with MATLAB
  • Author : Sukanta Nayak,Snehashish Chakraverty
  • Publisher :Unknown
  • Release Date :2018-02-05
  • Total pages :168
  • ISBN : 9780128129746
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Summary : 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

Computer Methods for Engineering with MATLAB® Applications, Second Edition

Computer Methods for Engineering with MATLAB® Applications, Second Edition
  • Author : Yogesh Jaluria
  • Publisher :Unknown
  • Release Date :2011-09-08
  • Total pages :631
  • ISBN : 9781591690368
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Summary : Substantially revised and updated, Computer Methods for Engineering with MATLAB® Applications, Second Edition presents equations to describe engineering processes and systems. It includes computer methods for solving these equations and discusses the nature and validity of the numerical results for a variety of engineering problems. This edition now uses MATLAB in its discussions of computer solution. New to the Second Edition Recent advances in computational software and hardware A large number of MATLAB commands and programs for solving exercises and to encourage students to develop their own computer programs for specific problems Additional exercises and examples in all chapters New and updated references The text follows a systematic approach for obtaining physically realistic, valid, and accurate results through numerical modeling. It employs examples from many engineering areas to explain the elements involved in the numerical solution and make the presentation relevant and interesting. It also incorporates a wealth of solved exercises to supplement the discussion and illustrate the ideas and methods presented. The book shows how a computational approach can provide physical insight and obtain inputs for the analysis and design of practical engineering systems.

Theories of Interval Arithmetic

Theories of Interval Arithmetic
  • Author : Hend Dawood
  • Publisher :Unknown
  • Release Date :2011-10-07
  • Total pages :128
  • ISBN : 9783846501542
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Summary : 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
  • Author : Joel H. Ferziger
  • Publisher :Unknown
  • Release Date :1981-10-09
  • Total pages :270
  • ISBN : UOM:39076005020396
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Summary : 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.

Differential Equations for Engineers

Differential Equations for Engineers
  • Author : Wei-Chau Xie
  • Publisher :Unknown
  • Release Date :2010-04-26
  • Total pages :229
  • ISBN : 9781139488167
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Summary : Xie presents a systematic introduction to ordinary differential equations for engineering students and practitioners. Mathematical concepts and various techniques are presented in a clear, logical, and concise manner. Various visual features are used to highlight focus areas. Complete illustrative diagrams are used to facilitate mathematical modeling of application problems. Readers are motivated by a focus on the relevance of differential equations through their applications in various engineering disciplines. Studies of various types of differential equations are determined by engineering applications. Theory and techniques for solving differential equations are then applied to solve practical engineering problems. A step-by-step analysis is presented to model the engineering problems using differential equations from physical principles and to solve the differential equations using the easiest possible method. This book is suitable for undergraduate students in engineering.

Computational Methods for Reliability and Risk Analysis

Computational Methods for Reliability and Risk Analysis
  • Author : Enrico Zio
  • Publisher :Unknown
  • Release Date :2009
  • Total pages :340
  • ISBN : 9789812839015
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Summary : This book illustrates a number of modelling and computational techniques for addressing relevant issues in reliability and risk analysis. In particular, it provides: i) a basic illustration of some methods used in reliability and risk analysis for modelling the stochastic failure and repair behaviour of systems, e.g. the Markov and Monte Carlo simulation methods; ii) an introduction to Genetic Algorithms, tailored to their application for RAMS (Reliability, Availability, Maintainability and Safety) optimization; iii) an introduction to key issues of system reliability and risk analysis, like dependent failures and importance measures; and iv) a presentation of the issue of uncertainty and of the techniques of sensitivity and uncertainty analysis used in support of reliability and risk analysis.The book provides a technical basis for senior undergraduate or graduate courses and a reference for researchers and practitioners in the field of reliability and risk analysis. Several practical examples are included to demonstrate the application of the concepts and techniques in practice.

Mathematical Reviews

Mathematical Reviews
  • Author : Anonim
  • Publisher :Unknown
  • Release Date :2006
  • Total pages :229
  • ISBN : UOM:39015068492381
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Summary :

Introduction to Computational Fluid Dynamics

Introduction to Computational Fluid Dynamics
  • Author : Atul Sharma
  • Publisher :Unknown
  • Release Date :2016-09-26
  • Total pages :300
  • ISBN : 9781119003038
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Summary : This book is primarily for a first one-semester course on CFD; in mechanical, chemical, and aeronautical engineering. Almost all the existing books on CFD assume knowledge of mathematics in general and differential calculus as well as numerical methods in particular; thus, limiting the readership mostly to the postgraduate curriculum. In this book, an attempt is made to simplify the subject even for readers who have little or no experience in CFD, and without prior knowledge of fluid-dynamics, heattransfer and numerical-methods. The major emphasis is on simplification of the mathematics involved by presenting physical-law (instead of the traditional differential equations) based algebraic-formulations, discussions, and solution-methodology. The physical law based simplified CFD approach (proposed in this book for the first time) keeps the level of mathematics to school education, and also allows the reader to intuitively get started with the computer-programming. Another distinguishing feature of the present book is to effectively link the theory with the computer-program (code). This is done with more pictorial as well as detailed explanation of the numerical methodology. Furthermore, the present book is structured for a module-by-module code-development of the two-dimensional numerical formulation; the codes are given for 2D heat conduction, advection and convection. The present subject involves learning to develop and effectively use a product - a CFD software. The details for the CFD development presented here is the main part of a CFD software. Furthermore, CFD application and analysis are presented by carefully designed example as well as exercise problems; not only limited to fluid dynamics but also includes heat transfer. The reader is trained for a job as CFD developer as well as CFD application engineer; and can also lead to start-ups on the development of "apps" (customized CFD software) for various engineering applications. "Atul has championed the finite volume method which is now the industry standard. He knows the conventional method of discretizing differential equations but has never been satisfied with it. As a result, he has developed a principle that physical laws that characterize the differential equations should be reflected at every stage of discretization and every stage of approximation. This new CFD book is comprehensive and has a stamp of originality of the author. It will bring students closer to the subject and enable them to contribute to it." —Dr. K. Muralidhar, IIT Kanpur, INDIA