Author: Manotosh Kumbhakar
Publisher: CRC Press
ISBN: 1000893359
Category : Technology & Engineering
Languages : en
Pages : 471
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Book Description
Most complex physical phenomena can be described by nonlinear equations, specifically, differential equations. In water engineering, nonlinear differential equations play a vital role in modeling physical processes. Analytical solutions to strong nonlinear problems are not easily tractable, and existing techniques are problem-specific and applicable for specific types of equations. Exploring the concept of homotopy from topology, different kinds of homotopy-based methods have been proposed for analytically solving nonlinear differential equations, given by approximate series solutions. Homotopy-Based Methods in Water Engineering attempts to present the wide applicability of these methods to water engineering problems. It solves all kinds of nonlinear equations, namely algebraic/transcendental equations, ordinary differential equations (ODEs), systems of ODEs, partial differential equations (PDEs), systems of PDEs, and integro-differential equations using the homotopy-based methods. The content of the book deals with some selected problems of hydraulics of open-channel flow (with or without sediment transport), groundwater hydrology, surface-water hydrology, general Burger’s equation, and water quality. Features: Provides analytical treatments to some key problems in water engineering Describes the applicability of homotopy-based methods for solving nonlinear equations, particularly differential equations Compares different approaches in dealing with issues of nonlinearity
Author: Shijun Liao
Publisher: Springer Science & Business Media
ISBN: 3642251323
Category : Mathematics
Languages : en
Pages : 566
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Book Description
"Homotopy Analysis Method in Nonlinear Differential Equations" presents the latest developments and applications of the analytic approximation method for highly nonlinear problems, namely the homotopy analysis method (HAM). Unlike perturbation methods, the HAM has nothing to do with small/large physical parameters. In addition, it provides great freedom to choose the equation-type of linear sub-problems and the base functions of a solution. Above all, it provides a convenient way to guarantee the convergence of a solution. This book consists of three parts. Part I provides its basic ideas and theoretical development. Part II presents the HAM-based Mathematica package BVPh 1.0 for nonlinear boundary-value problems and its applications. Part III shows the validity of the HAM for nonlinear PDEs, such as the American put option and resonance criterion of nonlinear travelling waves. New solutions to a number of nonlinear problems are presented, illustrating the originality of the HAM. Mathematica codes are freely available online to make it easy for readers to understand and use the HAM. This book is suitable for researchers and postgraduates in applied mathematics, physics, nonlinear mechanics, finance and engineering. Dr. Shijun Liao, a distinguished professor of Shanghai Jiao Tong University, is a pioneer of the HAM.
Author: Shijun Liao
Publisher: CRC Press
ISBN: 1135438293
Category : Mathematics
Languages : en
Pages : 335
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Book Description
Solving nonlinear problems is inherently difficult, and the stronger the nonlinearity, the more intractable solutions become. Analytic approximations often break down as nonlinearity becomes strong, and even perturbation approximations are valid only for problems with weak nonlinearity. This book introduces a powerful new analytic method for nonlinear problems-homotopy analysis-that remains valid even with strong nonlinearity. In Part I, the author starts with a very simple example, then presents the basic ideas, detailed procedures, and the advantages (and limitations) of homotopy analysis. Part II illustrates the application of homotopy analysis to many interesting nonlinear problems. These range from simple bifurcations of a nonlinear boundary-value problem to the Thomas-Fermi atom model, Volterra's population model, Von Karman swirling viscous flow, and nonlinear progressive waves in deep water. Although the homotopy analysis method has been verified in a number of prestigious journals, it has yet to be fully detailed in book form. Written by a pioneer in its development, Beyond Pertubation: Introduction to the Homotopy Analysis Method is your first opportunity to explore the details of this valuable new approach, add it to your analytic toolbox, and perhaps make contributions to some of the questions that remain open.
Author: Weicheng Cui
Publisher: Springer Nature
ISBN: 9811069468
Category : Technology & Engineering
Languages : en
Pages : 2203
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Book Description
This encyclopedia adopts a wider definition for the concept of ocean engineering. Specifically, it includes (1) offshore engineering: fixed and floating offshore oil and gas platforms; pipelines and risers; cables and moorings; buoy technology; foundation engineering; ocean mining; marine and offshore renewable energy; aquaculture engineering; and subsea engineering; (2) naval architecture: ship and special marine vehicle design; intact and damaged stability; technology for energy efficiency and green shipping; ship production technology; decommissioning and recycling; (3) polar and Arctic Engineering: ice mechanics; ice-structure interaction; polar operations; polar design; environmental protection; (4) underwater technologies: AUV/ROV design; AUV/ROV hydrodynamics; maneuvering and control; and underwater-specific communicating and sensing systems for AUV/ROVs. It summarizes the A–Z of the background and application knowledge of ocean engineering for use by ocean scientists and ocean engineers as well as nonspecialists such as engineers and scientists from all disciplines, economists, students, and politicians. Ocean engineering theories, ocean devices and equipment, ocean design and operation technologies are described by international experts, many from industry and each entry offers an introduction and references for further study, making current technology and operating practices available for future generations to learn from. The book also furthers our understanding of the current state of the art, leading to new and more efficient technologies with breakthroughs from new theory and materials. As the land resources approach the exploitation limit, ocean resources are becoming the next choice for the sustainable development. As such, ocean engineering is vital in the 21st century.
Author: Daniel T Valentine
Publisher: World Scientific
ISBN: 981448105X
Category : Science
Languages : en
Pages : 747
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Book Description
This volume presents more than 40 original papers on recent advances in several topics in engineering mechanics presented at The Theodore Y-T Wu Symposium on Engineering Mechanics: A celebration of Professor Wu's scientific contributions for his 80th birthday. The distinguished contributors include several members of the National Academy of Engineers and the topics cover nonlinear water waves, swimming and flying in nature, biomechanics, data analysis methodology, and propulsion hydrodynamics.The papers honor the significant accomplishments of Professor Wu in Engineering Science at Caltech, particularly in the areas of nonlinear waves, hydrodynamics, biomechanics and wave-structure interaction. They review the present state of the art of engineering mechanics, and chart the future of the field from the viewpoint of civil engineering, biomechanics, geophysics, mechanical engineering, naval architecture, ocean, and offshore engineering. The primary purpose of this book is to provide guidance and inspiration for those interested in continuing to advance engineering mechanics into the 21st century. To quote Professor Wu: ”The value of a book publication lies in disseminating new knowledge attained with effort and dedication from all those who participate, and in having the useful results within ready reach of students and researchers actively working in the field.”
Author: Shijun Liao
Publisher: World Scientific
ISBN: 9814551260
Category : Mathematics
Languages : en
Pages : 426
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Book Description
Unlike other analytic techniques, the Homotopy Analysis Method (HAM) is independent of small/large physical parameters. Besides, it provides great freedom to choose equation type and solution expression of related linear high-order approximation equations. The HAM provides a simple way to guarantee the convergence of solution series. Such uniqueness differentiates the HAM from all other analytic approximation methods. In addition, the HAM can be applied to solve some challenging problems with high nonlinearity.This book, edited by the pioneer and founder of the HAM, describes the current advances of this powerful analytic approximation method for highly nonlinear problems. Coming from different countries and fields of research, the authors of each chapter are top experts in the HAM and its applications.
Author: Vasile Marinca
Publisher: Springer
ISBN: 3319153749
Category : Technology & Engineering
Languages : en
Pages : 476
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Book Description
This book emphasizes in detail the applicability of the Optimal Homotopy Asymptotic Method to various engineering problems. It is a continuation of the book “Nonlinear Dynamical Systems in Engineering: Some Approximate Approaches”, published at Springer in 2011 and it contains a great amount of practical models from various fields of engineering such as classical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines and so on. The main structure of the book consists of 5 chapters. The first chapter is introductory while the second chapter is devoted to a short history of the development of homotopy methods, including the basic ideas of the Optimal Homotopy Asymptotic Method. The last three chapters, from Chapter 3 to Chapter 5, are introducing three distinct alternatives of the Optimal Homotopy Asymptotic Method with illustrative applications to nonlinear dynamical systems. The third chapter deals with the first alternative of our approach with two iterations. Five applications are presented from fluid mechanics and nonlinear oscillations. The Chapter 4 presents the Optimal Homotopy Asymptotic Method with a single iteration and solving the linear equation on the first approximation. Here are treated 32 models from different fields of engineering such as fluid mechanics, thermodynamics, nonlinear damped and undamped oscillations, electrical machines and even from physics and biology. The last chapter is devoted to the Optimal Homotopy Asymptotic Method with a single iteration but without solving the equation in the first approximation.
Author: Abdul-Majid Wazwaz
Publisher: Springer Science & Business Media
ISBN: 364200251X
Category : Mathematics
Languages : en
Pages : 746
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Book Description
"Partial Differential Equations and Solitary Waves Theory" is a self-contained book divided into two parts: Part I is a coherent survey bringing together newly developed methods for solving PDEs. While some traditional techniques are presented, this part does not require thorough understanding of abstract theories or compact concepts. Well-selected worked examples and exercises shall guide the reader through the text. Part II provides an extensive exposition of the solitary waves theory. This part handles nonlinear evolution equations by methods such as Hirota’s bilinear method or the tanh-coth method. A self-contained treatment is presented to discuss complete integrability of a wide class of nonlinear equations. This part presents in an accessible manner a systematic presentation of solitons, multi-soliton solutions, kinks, peakons, cuspons, and compactons. While the whole book can be used as a text for advanced undergraduate and graduate students in applied mathematics, physics and engineering, Part II will be most useful for graduate students and researchers in mathematics, engineering, and other related fields. Dr. Abdul-Majid Wazwaz is a Professor of Mathematics at Saint Xavier University, Chicago, Illinois, USA.
Author: Snehashish Chakraverty
Publisher: Springer
ISBN: 9811311536
Category : Computers
Languages : en
Pages : 184
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Book Description
This book addresses the basics of interval/fuzzy set theory, artificial neural networks (ANN) and computational methods. It presents step-by-step modeling for application problems along with simulation and numerical solutions. In general, every science and engineering problem is inherently biased by uncertainty, and there is often a need to model, solve and interpret problems in the world of uncertainty. At the same time, exact information about models and parameters of practical applications is usually not known and precise values do not exist. This book discusses uncertainty in both data and models. It consists of seven chapters covering various aspects of fuzzy uncertainty in application problems, such as shallow water wave equations, static structural problems, robotics, radon diffusion in soil, risk of invasive alien species and air quality quantification. These problems are handled by means of advanced computational and fuzzy theory along with machine intelligence when the uncertainties involved are fuzzy. The proposed computational methods offer new fuzzy computing methods that help other areas of knowledge construction where inexact information is present.
Author: Chu-Hui He
Publisher: Frontiers Media SA
ISBN: 2832539637
Category : Science
Languages : en
Pages : 132
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Book Description
The most well-known analytical method is the perturbation method, which has led to the great discovery of Neptune in 1846, and since then mathematical prediction and empirical observation became two sides of a coin in physics. However, the perturbation method is based on the small parameter assumption, and the obtained solutions are valid only for weakly nonlinear equations, which have greatly limited their applications to modern physical problems. To overcome the shortcomings, many mathematicians and physicists have been extensively developing various technologies for several centuries, however, there is no universal method for all nonlinear problems, and mathematical prediction with remarkably high accuracy is still much needed for modern physics, for example, the solitary waves traveling along an unsmooth boundary, the low-frequency property of a harvesting energy device, the pull-in voltage in a micro-electromechanical system. Now various effective analytical methods have appeared in the open literature, e.g., the homotopy perturbation method and the variational iteration method. An analytical solution provides a fast insight into its physical properties of a practical problem, e.g., frequency-amplitude relation of a nonlinear oscillator, solitary wave in an optical fiber, pull-in instability of a microelectromechanical system, making mathematical prediction even more attractive in modern physics. Nonlinear physics has been developing into a new stage, where the fractal-fractional differential equations have to be adopted to describe more accurately discontinuous problems, and it becomes ever more difficult to find an analytical solution for such nonlinear problems, and the analytical methods for fractal-fractional differential equations have laid the foundations for nonlinear physics.
