Decomposition Analysis Method In Linear And Nonlinear Differential Equations
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Decomposition Analysis Method In Linear And Nonlinear Differential Equations
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Author : Kansari Haldar
language : en
Publisher: CRC Press
Release Date : 2015-10-22
Decomposition Analysis Method In Linear And Nonlinear Differential Equations written by Kansari Haldar and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-22 with Mathematics categories.
A Powerful Methodology for Solving All Types of Differential EquationsDecomposition Analysis Method in Linear and Non-Linear Differential Equations explains how the Adomian decomposition method can solve differential equations for the series solutions of fundamental problems in physics, astrophysics, chemistry, biology, medicine, and other scientif
Solving Frontier Problems Of Physics The Decomposition Method
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Author : G. Adomian
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Solving Frontier Problems Of Physics The Decomposition Method written by G. Adomian 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 2013-06-29 with Science categories.
The Adomian decomposition method enables the accurate and efficient analytic solution of nonlinear ordinary or partial differential equations without the need to resort to linearization or perturbation approaches. It unifies the treatment of linear and nonlinear, ordinary or partial differential equations, or systems of such equations, into a single basic method, which is applicable to both initial and boundary-value problems. This volume deals with the application of this method to many problems of physics, including some frontier problems which have previously required much more computationally-intensive approaches. The opening chapters deal with various fundamental aspects of the decomposition method. Subsequent chapters deal with the application of the method to nonlinear oscillatory systems in physics, the Duffing equation, boundary-value problems with closed irregular contours or surfaces, and other frontier areas. The potential application of this method to a wide range of problems in diverse disciplines such as biology, hydrology, semiconductor physics, wave propagation, etc., is highlighted. For researchers and graduate students of physics, applied mathematics and engineering, whose work involves mathematical modelling and the quantitative solution of systems of equations.
Handbook Of Differential Equations
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Author : Daniel Zwillinger
language : en
Publisher: CRC Press
Release Date : 2021-12-30
Handbook Of Differential Equations written by Daniel Zwillinger and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-30 with Mathematics categories.
Through the previous three editions, Handbook of Differential Equations has proven an invaluable reference for anyone working within the field of mathematics, including academics, students, scientists, and professional engineers. The book is a compilation of methods for solving and approximating differential equations. These include the most widely applicable methods for solving and approximating differential equations, as well as numerous methods. Topics include methods for ordinary differential equations, partial differential equations, stochastic differential equations, and systems of such equations. Included for nearly every method are: The types of equations to which the method is applicable The idea behind the method The procedure for carrying out the method At least one simple example of the method Any cautions that should be exercised Notes for more advanced users The fourth edition includes corrections, many supplied by readers, as well as many new methods and techniques. These new and corrected entries make necessary improvements in this edition.
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.
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.
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.
Fourier Analysis And Nonlinear Partial Differential Equations
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Author : Hajer Bahouri
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-03
Fourier Analysis And Nonlinear Partial Differential Equations written by Hajer Bahouri 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 2011-01-03 with Mathematics categories.
In recent years, the Fourier analysis methods have expereinced a growing interest in the study of partial differential equations. In particular, those techniques based on the Littlewood-Paley decomposition have proved to be very efficient for the study of evolution equations. The present book aims at presenting self-contained, state- of- the- art models of those techniques with applications to different classes of partial differential equations: transport, heat, wave and Schrödinger equations. It also offers more sophisticated models originating from fluid mechanics (in particular the incompressible and compressible Navier-Stokes equations) or general relativity. It is either directed to anyone with a good undergraduate level of knowledge in analysis or useful for experts who are eager to know the benefit that one might gain from Fourier analysis when dealing with nonlinear partial differential equations.
Advances In Mathematical Modelling Applied Analysis And Computation
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Author : Jagdev Singh
language : en
Publisher: Springer Nature
Release Date : 2022-10-13
Advances In Mathematical Modelling Applied Analysis And Computation written by Jagdev Singh and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-13 with Technology & Engineering categories.
This book is a valuable source for graduate students and researchers and provides a comprehensive introduction to recent theories and applications of mathematical modeling and numerical simulation. It includes selected peer-reviewed papers presented at the 4th International Conference on Mathematical Modelling, Applied Analysis and Computation (ICMMAAC 2021), held at JECRC University, Jaipur, India, during August 5–7, 2021. The book is focused on mathematical modeling of various problems arising in science and engineering and new efficient numerical approaches for solving linear nonlinear problems and rigorous mathematical theories, which can be used to analyze different kinds of mathematical models. Applications of mathematical methods in physics, chemistry, biology, mechanical engineering, civil engineering, computer science, social science, and finance are presented.
Diversity Of Ecosystems
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Author : Mahamane Ali
language : en
Publisher: BoD – Books on Demand
Release Date : 2012-04-27
Diversity Of Ecosystems written by Mahamane Ali and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-27 with Science categories.
The ecosystems present a great diversity worldwide and use various functionalities according to ecologic regions. In this new context of variability and climatic changes, these ecosystems undergo notable modifications amplified by domestic uses of which it was subjected to. Indeed the ecosystems render diverse services to humanity from their composition and structure but the tolerable levels are unknown. The preservation of these ecosystemic services needs a clear understanding of their complexity. The role of research is not only to characterise the ecosystems but also to clearly define the tolerable usage levels. Their characterisation proves to be important not only for the local populations that use it but also for the conservation of biodiversity. Hence, the measurement, management and protection of ecosystems need innovative and diverse methods. For all these reasons, the aim of this book is to bring out a general view on the function of ecosystems, modelling, sampling strategies, invading species, the response of organisms to modifications, the carbon dynamics, the mathematical models and theories that can be applied in diverse conditions.
An Introduction To Domain Decomposition Methods
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Author : Victorita Dolean
language : en
Publisher: SIAM
Release Date : 2015-12-08
An Introduction To Domain Decomposition Methods written by Victorita Dolean and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-08 with Science categories.
The purpose of this book is to offer an overview of the most popular domain decomposition methods for partial differential equations (PDEs). These methods are widely used for numerical simulations in solid mechanics, electromagnetism, flow in porous media, etc., on parallel machines from tens to hundreds of thousands of cores. The appealing feature of domain decomposition methods is that, contrary to direct methods, they are naturally parallel. The authors focus on parallel linear solvers. The authors present all popular algorithms, both at the PDE level and at the discrete level in terms of matrices, along with systematic scripts for sequential implementation in a free open-source finite element package as well as some parallel scripts. Also included is a new coarse space construction (two-level method) that adapts to highly heterogeneous problems.