# Computational Interval Methods for Engineering Applications

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

Produk Detail:

• Author : Snehashish Chakraverty
• Pages : 220 pages
• ISBN : 0128178590
• Rating : 5/5 from 3 reviews

## Computational Interval Methods for Engineering Applications

• Author : Snehashish Chakraverty,Nisha Rani Mahato
• Release : 01 November 2020

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

## Computational Intelligence in Information Assurance and Security

• Author : Ajith Abraham
• Publisher : Springer
• Release : 04 May 2007

This volume provides the academic and industrial community with a medium for presenting original research and applications related to information assurance and security using computational intelligence techniques. It details current research on information assurance and security regarding both the theoretical and methodological aspects, as well as various applications in solving real world problems using computational intelligence.

## Scientific Computing, Validated Numerics, Interval Methods

• Author : Walter Krämer,Jürgen Wolff von Gudenberg
• Publisher : Springer Science & Business Media
• Release : 17 April 2013

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,

## Soft Computing Approach for Mathematical Modeling of Engineering Problems

• Author : Ali Ahmadian,Soheil Salahshour
• Publisher : CRC Press
• Release : 03 September 2021

This book describes different mathematical modeling and soft computing techniques used to solve practical engineering problems. It gives an overview of the current state of soft computing techniques and describes the advantages and disadvantages of soft computing compared to traditional hard computing techniques. Through examples and case studies the editors demonstrate and describe how problems with inherent uncertainty can be addressed and eventually solved through the aid of numerical models and methods. The chapters address several applications and examples in

## Methods and Applications of Interval Analysis

• Author : Ramon E. Moore
• Publisher : SIAM
• Release : 01 January 1979

This book treats an important set of techniques that provide a mathematically rigorous and complete error analysis for computational results. It shows that interval analysis provides a powerful set of tools with direct applicability to important problems in scientific computing.

## Interval Methods for Circuit Analysis

• Author : L. V. Kolev
• Publisher : World Scientific
• Release : 17 May 1993

Written by an electrical engineer this book presents a novel approach in electric circuit theory which is based on interval analysis ? an intensively developing branch or applied mathematics. Covering major topics in both circuit and system theory and their applications, it suggests a variety of methods that are suited for handling linear and nonlinear analysis problems in which some or all of the relevant data are given as intervals. Detailed algorithms of the interval methods presented are developed, enabling their

## Inclusion Methods for Nonlinear Problems

• Author : Jürgen Herzberger
• Publisher : Springer Science & Business Media
• Release : 06 December 2012

This workshop was organized with the support of GAMM, the International Association of Applied Mathematics and Mechanics, on the occasion of J. Herzberger's 60th birthday. GAMM is thankful to him for all the time and work he spent in the preparation and holding of the meeting. The talks presented during the workshop and the papers published in this volume are part of the field of Verification Numerics. The important subject is fostered by GAMM already since a number of years,

## Interval Methods for Solving Nonlinear Constraint Satisfaction, Optimization and Similar Problems

• Author : Bartłomiej Jacek Kubica
• Publisher : Springer
• Release : 08 March 2019

This book highlights recent research on interval methods for solving nonlinear constraint satisfaction, optimization and similar problems. Further, it presents a comprehensive survey of applications in various branches of robotics, artificial intelligence systems, economics, control theory, dynamical systems theory, and others. Three appendices, on the notation, representation of numbers used as intervals’ endpoints, and sample implementations of the interval data type in several programming languages, round out the coverage.

## Applications of Interval Computations

• Author : R. Baker Kearfott,V. Kreinovich
• Publisher : Springer Science & Business Media
• Release : 01 December 2013

Primary Audience for the Book • Specialists in numerical computations who are interested in algorithms with automatic result verification. • Engineers, scientists, and practitioners who desire results with automatic verification and who would therefore benefit from the experience of suc cessful applications. • Students in applied mathematics and computer science who want to learn these methods. Goal Of the Book This book contains surveys of applications of interval computations, i. e. , appli cations of numerical methods with automatic result verification, that were pre

## Scientific Computing, Computer Arithmetic, and Validated Numerics

• Author : Marco Nehmeier,Jürgen Wolff von Gudenberg,Warwick Tucker
• Publisher : Springer
• Release : 08 April 2016

This book constitutes the refereed post proceedings of the 16th International Symposium, SCAN 2014, held in Würzburg, Germany, in September 2014. The 22 full papers presented were carefully reviewed and selected from 60 submissions. The main concerns of research addressed by SCAN conferences are validation, verification or reliable assertions of numerical computations. Interval arithmetic and other treatments of uncertainty are developed as appropriate tools.

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

• Author : Andrew Pownuk,Vladik Kreinovich
• Publisher : Springer
• Release : 03 May 2018

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

## The Finite Element Method

• Author : Zhangxin Chen
• Publisher : World Scientific Publishing Company
• Release : 06 October 2011

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

## Advances in Computation and Intelligence

• Author : Sanyou Zeng
• Publisher : Springer
• Release : 26 August 2007

This book constitutes the refereed proceedings of the Second International Symposium on Intelligence Computation and Applications, ISICA 2007, held in Wuhan, China, in September 2007. The 71 revised full papers cover such topics as evolutionary computation, evolutionary learning, neural networks, swarms, pattern recognition, and data mining.

## Knowledge Processing with Interval and Soft Computing

• Author : Chenyi Hu,R. Baker Kearfott,Andre de Korvin,Vladik Kreinovich
• Publisher : Springer Science & Business Media
• Release : 03 April 2009

Interval computing combined with fuzzy logic has become an emerging tool in studying artificial intelligence and knowledge processing (AIKP) applications since it models uncertainties frequently raised in the field. This book provides introductions for both interval and fuzzy computing in a very accessible style. Application algorithms covered in this book include quantitative and qualitative data mining with interval valued datasets, decision making systems with interval valued parameters, interval valued Nash games and interval weighted graphs. Successful applications in studying finance