Fuzzy Differential Equations And Applications For Engineers And Scientists
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Fuzzy Differential Equations And Applications For Engineers And Scientists
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Author : Snehashish Chakraverty
language : en
Publisher:
Release Date : 2016
Fuzzy Differential Equations And Applications For Engineers And Scientists written by Snehashish Chakraverty and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Differential equations categories.
Fuzzy Differential Equations And Applications For Engineers And Scientists
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Author : S. Chakraverty
language : en
Publisher: CRC Press
Release Date : 2016-11-25
Fuzzy Differential Equations And Applications For Engineers And Scientists written by S. Chakraverty and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-25 with Mathematics categories.
Differential equations play a vital role in the modeling of physical and engineering problems, such as those in solid and fluid mechanics, viscoelasticity, biology, physics, and many other areas. In general, the parameters, variables and initial conditions within a model are considered as being defined exactly. In reality there may be only vague, imprecise or incomplete information about the variables and parameters available. This can result from errors in measurement, observation, or experimental data; application of different operating conditions; or maintenance induced errors. To overcome uncertainties or lack of precision, one can use a fuzzy environment in parameters, variables and initial conditions in place of exact (fixed) ones, by turning general differential equations into Fuzzy Differential Equations ("FDEs"). In real applications it can be complicated to obtain exact solution of fuzzy differential equations due to complexities in fuzzy arithmetic, creating the need for use of reliable and efficient numerical techniques in the solution of fuzzy differential equations. These include fuzzy ordinary and partial, fuzzy linear and nonlinear, and fuzzy arbitrary order differential equations. This unique work?provides a new direction for the reader in the use of basic concepts of fuzzy differential equations, solutions and its applications. It can serve as an essential reference work for students, scholars, practitioners, researchers and academicians in engineering and science who need to model uncertain physical problems.
Advanced Numerical And Semi Analytical Methods For Differential Equations
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Author : Snehashish Chakraverty
language : en
Publisher: John Wiley & Sons
Release Date : 2019-04-16
Advanced Numerical And Semi Analytical Methods For Differential Equations written by Snehashish Chakraverty and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-16 with Mathematics categories.
Examines numerical and semi-analytical methods for differential equations that can be used for solving practical ODEs and PDEs This student-friendly book deals with various approaches for solving differential equations numerically or semi-analytically depending on the type of equations and offers simple example problems to help readers along. Featuring both traditional and recent methods, Advanced Numerical and Semi Analytical Methods for Differential Equations begins with a review of basic numerical methods. It then looks at Laplace, Fourier, and weighted residual methods for solving differential equations. A new challenging method of Boundary Characteristics Orthogonal Polynomials (BCOPs) is introduced next. The book then discusses Finite Difference Method (FDM), Finite Element Method (FEM), Finite Volume Method (FVM), and Boundary Element Method (BEM). Following that, analytical/semi analytic methods like Akbari Ganji's Method (AGM) and Exp-function are used to solve nonlinear differential equations. Nonlinear differential equations using semi-analytical methods are also addressed, namely Adomian Decomposition Method (ADM), Homotopy Perturbation Method (HPM), Variational Iteration Method (VIM), and Homotopy Analysis Method (HAM). Other topics covered include: emerging areas of research related to the solution of differential equations based on differential quadrature and wavelet approach; combined and hybrid methods for solving differential equations; as well as an overview of fractal differential equations. Further, uncertainty in term of intervals and fuzzy numbers have also been included, along with the interval finite element method. This book: Discusses various methods for solving linear and nonlinear ODEs and PDEs Covers basic numerical techniques for solving differential equations along with various discretization methods Investigates nonlinear differential equations using semi-analytical methods Examines differential equations in an uncertain environment Includes a new scenario in which uncertainty (in term of intervals and fuzzy numbers) has been included in differential equations Contains solved example problems, as well as some unsolved problems for self-validation of the topics covered Advanced Numerical and Semi Analytical Methods for Differential Equations is an excellent text for graduate as well as post graduate students and researchers studying various methods for solving differential equations, numerically and semi-analytically.
Mathematics In Engineering Sciences
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Author : Mangey Ram
language : en
Publisher: CRC Press
Release Date : 2019-09-09
Mathematics In Engineering Sciences written by Mangey Ram and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-09 with Mathematics categories.
This book includes research studies, novel theory, as well as new methodology and applications in mathematics and management sciences. The book will provide a comprehensive range of mathematics applied to engineering areas for different tasks. It will offer an international perspective and a bridge between classical theory and new methodology in many areas, along with real-life applications. Features Offers solutions to multi-objective transportation problem under cost reliability using utility function Presents optimization techniques to support eco-efficiency assessment in manufacturing processes Covers distance-based function approach for optimal design of engineering processes with multiple quality characteristics Provides discrete time sliding mode control for non-linear networked control systems Discusses second law of thermodynamics as instruments for optimizing fluid dynamic systems and aerodynamic systems
Fuzzy Mathematics In Economics And Engineering
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Author : James J. Buckley
language : en
Publisher: Physica
Release Date : 2013-06-05
Fuzzy Mathematics In Economics And Engineering written by James J. Buckley and has been published by Physica this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-05 with Business & Economics categories.
The book aims at surveying results in the application of fuzzy sets and fuzzy logic to economics and engineering. New results include fuzzy non-linear regression, fully fuzzified linear programming, fuzzy multi-period control, fuzzy network analysis, each using an evolutionary algorithm; fuzzy queuing decision analysis using possibility theory; fuzzy differential equations; fuzzy difference equations; fuzzy partial differential equations; fuzzy eigenvalues based on an evolutionary algorithm; fuzzy hierarchical analysis using an evolutionary algorithm; fuzzy integral equations. Other important topics covered are fuzzy input-output analysis; fuzzy mathematics of finance; fuzzy PERT (project evaluation and review technique). No previous knowledge of fuzzy sets is needed. The mathematical background is assumed to be elementary calculus.
Applications Of Hybrid Nanofluids In Science And Engineering
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Author : A. K. Pandey
language : en
Publisher: CRC Press
Release Date : 2025-03-18
Applications Of Hybrid Nanofluids In Science And Engineering written by A. K. Pandey and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-18 with Science categories.
Applications of Hybrid Nanofluids in Science and Engineering delves deep into the multifaceted realms in which these dynamic fluids are playing a pivotal role in various fields. This comprehensive volume elucidates the diverse applications and promising potentials of hybrid nanofluids. It introduces hybrid nanofluids and their preparation methods, thermophysical properties, advantages, applications, and future scope. Models to compute the effective thermophysical properties of hybrid nanofluids are also discussed, along with their limitations. In the application section, mathematical models are formulated to contemplate the flow of hybrid nanofluids through different surfaces/geometries under different situations. Also, the entropy generation minimization in hybrid nanofluid flow is discussed with its application in refrigeration, power generation, and other processes. The subject matter in this book will enable the reader to do the following: Learn the ins and outs of hybrid nanofluids—from how they are made to the special characteristics they embody Explore hybrid nanofluids' potential in thermal management, energy systems, materials science, biomedical engineering, and more Use advanced computational and analytical methods to analyse complex fluid dynamics models Anticipate the impact of hybrid nanofluid research on upcoming sectors like renewable energy and innovative manufacturing This book is aimed at researchers and graduate students in mechanical and chemical engineering and materials science.
Artificial Neural Networks And Type 2 Fuzzy Set
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Author : Snehashish Chakraverty
language : en
Publisher: Elsevier
Release Date : 2025-03-06
Artificial Neural Networks And Type 2 Fuzzy Set written by Snehashish Chakraverty and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-06 with Computers categories.
Soft computing is an emerging discipline which aims to exploit tolerance for imprecision, approximate reasoning, and uncertainty to achieve robustness, tractability, and cost effectiveness for building intelligent machines. Soft computing methodologies include neural networks, fuzzy sets, genetic algorithms, Bayesian networks, and rough sets, among others. In this regard, neural networks are widely used for modeling dynamic solvers, classification of data, and prediction of solutions, whereas fuzzy sets provide a natural framework for dealing with uncertainty. Artificial Neural Networks and Type-2 Fuzzy Set: Elements of Soft Computing and Its Applications covers the fundamental concepts and the latest research on variants of Artificial Neural Networks (ANN), including scientific machine learning and Type-2 Fuzzy Set (T2FS). In addition, the book also covers different applications for solving real-world problems along with various examples and case studies. It may be noted that quite a bit of research has been done on ANN and Fuzzy Set theory/ Fuzzy logic. However, Artificial Neural Networks and Type-2 Fuzzy Set is the first book to cover the use of ANN and fuzzy set theory with regards to Type-2 Fuzzy Set in static and dynamic problems in one place. Artificial Neural Networks and Type-2 Fuzzy Sets are two of the most widely used computational intelligence techniques for solving complex problems in various domains. Both ANN and T2FS have unique characteristics that make them suitable for different types of problems. This book provides the reader with in-depth understanding of how to apply these computational intelligence techniques in various fields of science and engineering in general and static and dynamic problems in particular. Further, for validation purposes of the ANN and fuzzy models, the obtained solutions of each model in the book is compared with already existing solutions that have been obtained with numerical or analytical methods. - Covers the fundamental concepts and the latest research on variants of Artificial Neural Networks, including scientific machine learning and Type-2 Fuzzy Set - Discusses the integration of ANN and Type-2 Fuzzy Set, showing how combining these two approaches can enhance the performance and robustness of intelligent systems - Demonstrates how to solve scientific and engineering research problems through a variety of real-world examples and case studies - Includes coverage of both static and dynamic problems, along with validation of ANN and Fuzzy models by comparing the obtained solutions of each model with already existing solutions that have been obtained with numerical or analytical methods
Advances In Differential And Difference Equations With Applications 2020
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Author : Dumitru Baleanu
language : en
Publisher: MDPI
Release Date : 2021-01-20
Advances In Differential And Difference Equations With Applications 2020 written by Dumitru Baleanu and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-20 with Computers categories.
It is very well known that differential equations are related with the rise of physical science in the last several decades and they are used successfully for models of real-world problems in a variety of fields from several disciplines. Additionally, difference equations represent the discrete analogues of differential equations. These types of equations started to be used intensively during the last several years for their multiple applications, particularly in complex chaotic behavior. A certain class of differential and related difference equations is represented by their respective fractional forms, which have been utilized to better describe non-local phenomena appearing in all branches of science and engineering. The purpose of this book is to present some common results given by mathematicians together with physicists, engineers, as well as other scientists, for whom differential and difference equations are valuable research tools. The reported results can be used by researchers and academics working in both pure and applied differential equations.
New Paradigms In Computational Modeling And Its Applications
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Author : Snehashish Chakraverty
language : en
Publisher: Academic Press
Release Date : 2021-01-09
New Paradigms In Computational Modeling And Its Applications written by Snehashish Chakraverty and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-09 with Science categories.
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
Affine Arithmetic Based Solution Of Uncertain Static And Dynamic Problems
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Author : Snehashish Chakraverty
language : en
Publisher: Springer Nature
Release Date : 2022-05-31
Affine Arithmetic Based Solution Of Uncertain Static And Dynamic Problems written by Snehashish Chakraverty and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-31 with Mathematics categories.
Uncertainty is an inseparable component of almost every measurement and occurrence when dealing with real-world problems. Finding solutions to real-life problems in an uncertain environment is a difficult and challenging task. As such, this book addresses the solution of uncertain static and dynamic problems based on affine arithmetic approaches. Affine arithmetic is one of the recent developments designed to handle such uncertainties in a different manner which may be useful for overcoming the dependency problem and may compute better enclosures of the solutions. Further, uncertain static and dynamic problems turn into interval and/or fuzzy linear/nonlinear systems of equations and eigenvalue problems, respectively. Accordingly, this book includes newly developed efficient methods to handle the said problems based on the affine and interval/fuzzy approach. Various illustrative examples concerning static and dynamic problems of structures have been investigated in order to showthe reliability and efficacy of the developed approaches.