Homotopy Asymptotic Method And Its Application
Download Homotopy Asymptotic Method And Its Application full books in PDF, epub, and Kindle. Read online free Homotopy Asymptotic Method And Its Application ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads.
Author |
: Vasile Marinca |
Publisher |
: Springer |
Total Pages |
: 476 |
Release |
: 2015-04-02 |
ISBN-10 |
: 9783319153742 |
ISBN-13 |
: 3319153749 |
Rating |
: 4/5 (42 Downloads) |
Synopsis The Optimal Homotopy Asymptotic Method by : Vasile Marinca
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 |
: Baojian Hong |
Publisher |
: |
Total Pages |
: |
Release |
: 2017 |
ISBN-10 |
: OCLC:1154219055 |
ISBN-13 |
: |
Rating |
: 4/5 (55 Downloads) |
Synopsis Homotopy Asymptotic Method and Its Application by : Baojian Hong
As we all know, perturbation theory is closely related to methods used in the numerical analysis fields. In this chapter, we focus on introducing two homotopy asymptotic methods and their applications. In order to search for analytical approximate solutions of two types of typical nonlinear partial differential equations by using the famous homotopy analysis method (HAM) and the homotopy perturbation method (HPM), we consider these two systems including the generalized perturbed Kortewerg-de Vries-Burgers equation and the generalized perturbed nonlinear Schrödinger equation (GPNLS). The approximate solution with arbitrary degree of accuracy for these two equations is researched, and the efficiency, accuracy and convergence of the approximate solution are also discussed.
Author |
: Shijun Liao |
Publisher |
: World Scientific |
Total Pages |
: 426 |
Release |
: 2013-11-26 |
ISBN-10 |
: 9789814551267 |
ISBN-13 |
: 9814551260 |
Rating |
: 4/5 (67 Downloads) |
Synopsis Advances In The Homotopy Analysis Method by : Shijun Liao
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 |
: Muhammad Idrees |
Publisher |
: LAP Lambert Academic Publishing |
Total Pages |
: 108 |
Release |
: 2012-06 |
ISBN-10 |
: 3848496607 |
ISBN-13 |
: 9783848496600 |
Rating |
: 4/5 (07 Downloads) |
Synopsis Optimal Homotopy Asymptotic Method by : Muhammad Idrees
The objective of this work is to use Optimal Homotopy Asymptotic Method (OHAM), a new semi-analytic approximating technique, for solving linear and nonlinear initial and boundary value problems. The semi analytic solutions of nonlinear fourth order, eighth order, special fourth order and special sixth order boundary-value problems are computed using OHAM. Successful application of OHAM for squeezing flow is a major task in this study. This work also investigates the effectiveness of OHAM formulation for Partial Differential Equations (Wave Equation and Korteweg de Vries). OHAM is independent of the free parameter and there is no need of the initial guess as there is in Homotopy Perturbation Method (HPM), Variational Iteration Method (VIM) and Homotopy Analysis Method (HAM). OHAM works very well with large domains and provides better accuracy at lower-order of approximations. Moreover, the convergence domain can be easily adjusted. The results are compared with other methods like HPM, VIM and HAM, which reveal that OHAM is effective, simpler, easier and explicit.
Author |
: Shijun Liao |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 566 |
Release |
: 2012-06-22 |
ISBN-10 |
: 9783642251320 |
ISBN-13 |
: 3642251323 |
Rating |
: 4/5 (20 Downloads) |
Synopsis Homotopy Analysis Method in Nonlinear Differential Equations by : Shijun Liao
"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 |
: Igor Andrianov |
Publisher |
: John Wiley & Sons |
Total Pages |
: 281 |
Release |
: 2014-02-06 |
ISBN-10 |
: 9781118725146 |
ISBN-13 |
: 111872514X |
Rating |
: 4/5 (46 Downloads) |
Synopsis Asymptotic Methods in the Theory of Plates with Mixed Boundary Conditions by : Igor Andrianov
Asymptotic Methods in the Theory of Plates with Mixed Boundary Conditions comprehensively covers the theoretical background of asymptotic approaches and their use in solving mechanical engineering-oriented problems of structural members, primarily plates (statics and dynamics) with mixed boundary conditions. The first part of this book introduces the theory and application of asymptotic methods and includes a series of approaches that have been omitted or not rigorously treated in the existing literature. These lesser known approaches include the method of summation and construction of the asymptotically equivalent functions, methods of small and large delta, and the homotopy perturbations method. The second part of the book contains original results devoted to the solution of the mixed problems of the theory of plates, including statics, dynamics and stability of the studied objects. In addition, the applicability of the approaches presented to other related linear or nonlinear problems is addressed. Key features: • Includes analytical solving of mixed boundary value problems • Introduces modern asymptotic and summation procedures • Presents asymptotic approaches for nonlinear dynamics of rods, beams and plates • Covers statics, dynamics and stability of plates with mixed boundary conditions • Explains links between the Adomian and homotopy perturbation approaches Asymptotic Methods in the Theory of Plates with Mixed Boundary Conditions is a comprehensive reference for researchers and practitioners working in the field of Mechanics of Solids and Mechanical Engineering, and is also a valuable resource for graduate and postgraduate students from Civil and Mechanical Engineering.
Author |
: Shijun Liao |
Publisher |
: CRC Press |
Total Pages |
: 335 |
Release |
: 2003-10-27 |
ISBN-10 |
: 9781135438296 |
ISBN-13 |
: 1135438293 |
Rating |
: 4/5 (96 Downloads) |
Synopsis Beyond Perturbation by : Shijun Liao
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 |
: Santanu Saha Ray |
Publisher |
: CRC Press |
Total Pages |
: 251 |
Release |
: 2018-01-12 |
ISBN-10 |
: 9781351682213 |
ISBN-13 |
: 1351682210 |
Rating |
: 4/5 (13 Downloads) |
Synopsis Wavelet Methods for Solving Partial Differential Equations and Fractional Differential Equations by : Santanu Saha Ray
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.
Author |
: Dimo Uzunov |
Publisher |
: BoD – Books on Demand |
Total Pages |
: 202 |
Release |
: 2017-06-14 |
ISBN-10 |
: 9789535132615 |
ISBN-13 |
: 953513261X |
Rating |
: 4/5 (15 Downloads) |
Synopsis Recent Studies inPerturbation Theory by : Dimo Uzunov
The book contains seven chapters written by noted experts and young researchers who present their recent studies of both pure mathematical problems of perturbation theories and application of perturbation methods to the study of the important topic in physics, for example, renormalization group theory and applications to basic models in theoretical physics (Y. Takashi), the quantum gravity and its detection and measurement (F. Bulnes), atom-photon interactions (E. G. Thrapsaniotis), treatment of spectra and radiation characteristics by relativistic perturbation theory (A. V. Glushkov et al), and Green's function theory and some applications (Jing Huang). The pure mathematical issues are related to the problem of generalization of the boundary layer function method for bisingularly perturbed differential equations (K. Alymkulov and D. A. Torsunov) and to the development of new homotopy asymptotic methods and some of their applications (Baojian Hong).
Author |
: Jagdev Singh |
Publisher |
: Springer Nature |
Total Pages |
: 397 |
Release |
: |
ISBN-10 |
: 9783031563072 |
ISBN-13 |
: 3031563077 |
Rating |
: 4/5 (72 Downloads) |
Synopsis Advances in Mathematical Modelling, Applied Analysis and Computation by : Jagdev Singh