Homotopy Analysis Method In Nonlinear Differential Equations
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Homotopy Analysis Method In Nonlinear Differential Equations
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Author : Shijun Liao
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-06-22
Homotopy Analysis Method In Nonlinear Differential Equations written by Shijun Liao and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-22 with Mathematics categories.
"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.
Advances In The Homotopy Analysis Method
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Author : Shijun Liao
language : en
Publisher: World Scientific
Release Date : 2013-11-26
Advances In The Homotopy Analysis Method written by Shijun Liao and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-26 with Mathematics categories.
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.
Nonlinear Flow Phenomena And Homotopy Analysis
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Author : Kuppalapalle Vajravelu
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-22
Nonlinear Flow Phenomena And Homotopy Analysis written by Kuppalapalle Vajravelu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-22 with Mathematics categories.
Since most of the problems arising in science and engineering are nonlinear, they are inherently difficult to solve. Traditional analytical approximations are valid only for weakly nonlinear problems and often fail when used for problems with strong nonlinearity. “Nonlinear Flow Phenomena and Homotopy Analysis: Fluid Flow and Heat Transfer” presents the current theoretical developments of the analytical method of homotopy analysis. This book not only addresses the theoretical framework for the method, but also gives a number of examples of nonlinear problems that have been solved by means of the homotopy analysis method. The particular focus lies on fluid flow problems governed by nonlinear differential equations. This book is intended for researchers in applied mathematics, physics, mechanics and engineering. Both Kuppalapalle Vajravelu and Robert A. Van Gorder work at the University of Central Florida, USA.
Analytical Methods In Nonlinear Oscillations
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Author : Ebrahim Esmailzadeh
language : en
Publisher: Springer
Release Date : 2018-06-29
Analytical Methods In Nonlinear Oscillations written by Ebrahim Esmailzadeh and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-29 with Technology & Engineering categories.
This book covers both classical and modern analytical methods in nonlinear systems. A wide range of applications from fundamental research to engineering problems are addressed. The book contains seven chapters, each with miscellaneous problems and their detailed solutions. More than 100 practice problems are illustrated, which might be useful for students and researchers in the areas of nonlinear oscillations and applied mathematics. With providing real world examples, this book shows the multidisciplinary emergence of nonlinear dynamical systems in a wide range of applications including mechanical and electrical oscillators, micro/nano resonators and sensors, and also modelling of global warming, epidemic diseases, sociology, chemical reactions, biology and ecology.
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.
Wavelet Methods For Solving Partial Differential Equations And Fractional Differential Equations
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Author : Santanu Saha Ray
language : en
Publisher: CRC Press
Release Date : 2018-01-12
Wavelet Methods For Solving Partial Differential Equations And Fractional Differential Equations written by Santanu Saha Ray and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-12 with Mathematics categories.
The main focus of the book is to implement wavelet based transform methods for solving problems of fractional order partial differential equations arising in modelling real physical phenomena. It explores analytical and numerical approximate solution obtained by wavelet methods for both classical and fractional order partial differential equations.
Analytical Methods For Nonlinear Oscillators And Solitary Waves
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Author : Chu-Hui He
language : en
Publisher: Frontiers Media SA
Release Date : 2023-11-24
Analytical Methods For Nonlinear Oscillators And Solitary Waves written by Chu-Hui He and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-24 with Science categories.
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.
Beyond Perturbation
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Author : Shijun Liao
language : en
Publisher: CRC Press
Release Date : 2003-10-27
Beyond Perturbation written by Shijun Liao and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-10-27 with Mathematics categories.
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
Analysis Geometry Nonlinear Optimization And Applications
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Author : Panos M Pardalos
language : en
Publisher: World Scientific
Release Date : 2023-03-20
Analysis Geometry Nonlinear Optimization And Applications written by Panos M Pardalos and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-20 with Mathematics categories.
This volume features an extensive account of both research and expository papers in a wide area of engineering and mathematics and its various applications.Topics treated within this book include optimization of control points, game theory, equilibrium points, algorithms, Cartan matrices, integral inequalities, Volterra integro-differential equations, Caristi-Kirk theorems, Laplace type integral operators, etc.This useful reference text benefits graduate students, beginning research engineers and mathematicians as well as established researchers in these domains.
Numerical And Analytical Solutions For Solving Nonlinear Equations In Heat Transfer
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Author : Ganji, Davood Domiri
language : en
Publisher: IGI Global
Release Date : 2017-07-26
Numerical And Analytical Solutions For Solving Nonlinear Equations In Heat Transfer written by Ganji, Davood Domiri and has been published by IGI Global this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-26 with Technology & Engineering categories.
Engineering applications offer benefits and opportunities across a range of different industries and fields. By developing effective methods of analysis, results and solutions are produced with higher accuracy. Numerical and Analytical Solutions for Solving Nonlinear Equations in Heat Transfer is an innovative source of academic research on the optimized techniques for analyzing heat transfer equations and the application of these methods across various fields. Highlighting pertinent topics such as the differential transformation method, industrial applications, and the homotopy perturbation method, this book is ideally designed for engineers, researchers, graduate students, professionals, and academics interested in applying new mathematical techniques in engineering sciences.