The Optimal Homotopy Asymptotic Method

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The Optimal Homotopy Asymptotic Method

Vasile Marinca,Nicolae Herisanu
The Optimal Homotopy Asymptotic Method Book PDF

Author : Vasile Marinca,Nicolae Herisanu
Publisher : Springer
Page : 476 pages
File Size : 47,7 Mb
Release : 2015-04-02
Category : Technology & Engineering
ISBN : 9783319153742

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The Optimal Homotopy Asymptotic Method by Vasile Marinca,Nicolae Herisanu Pdf

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.

Homotopy Analysis Method in Nonlinear Differential Equations

Shijun Liao
Homotopy Analysis Method in Nonlinear Differential Equations Book PDF

Author : Shijun Liao
Publisher : Springer Science & Business Media
Page : 566 pages
File Size : 54,7 Mb
Release : 2012-06-22
Category : Mathematics
ISBN : 9783642251320

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Homotopy Analysis Method in Nonlinear Differential Equations by Shijun Liao Pdf

"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.

Fuzzy Fractional Differential Operators and Equations

Tofigh Allahviranloo
Fuzzy Fractional Differential Operators and Equations Book PDF

Author : Tofigh Allahviranloo
Publisher : Springer Nature
Page : 303 pages
File Size : 55,9 Mb
Release : 2020-06-15
Category : Technology & Engineering
ISBN : 9783030512729

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Fuzzy Fractional Differential Operators and Equations by Tofigh Allahviranloo Pdf

This book contains new and useful materials concerning fuzzy fractional differential and integral operators and their relationship. As the title of the book suggests, the fuzzy subject matter is one of the most important tools discussed. Therefore, it begins by providing a brief but important and new description of fuzzy sets and the computational calculus they require. Fuzzy fractals and fractional operators have a broad range of applications in the engineering, medical and economic sciences. Although these operators have been addressed briefly in previous papers, this book represents the first comprehensive collection of all relevant explanations. Most of the real problems in the biological and engineering sciences involve dynamic models, which are defined by fuzzy fractional operators in the form of fuzzy fractional initial value problems. Another important goal of this book is to solve these systems and analyze their solutions both theoretically and numerically. Given the content covered, the book will benefit all researchers and students in the mathematical and computer sciences, but also the engineering sciences.

Nonlinear Dynamical Systems in Engineering

Vasile Marinca,Nicolae Herisanu
Nonlinear Dynamical Systems in Engineering Book PDF

Author : Vasile Marinca,Nicolae Herisanu
Publisher : Springer Science & Business Media
Page : 403 pages
File Size : 48,6 Mb
Release : 2012-01-05
Category : Technology & Engineering
ISBN : 9783642227349

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Nonlinear Dynamical Systems in Engineering by Vasile Marinca,Nicolae Herisanu Pdf

This book presents and extend different known methods to solve different types of strong nonlinearities encountered by engineering systems. A better knowledge of the classical methods presented in the first part lead to a better choice of the so-called “base functions”. These are absolutely necessary to obtain the auxiliary functions involved in the optimal approaches which are presented in the second part. Every chapter introduces a distinct approximate method applicable to nonlinear dynamical systems. Each approximate analytical approach is accompanied by representative examples related to nonlinear dynamical systems from to various fields of engineering.

Nonlinear Dynamical Systems in Engineering

Vasile Marinca,Nicolae Herisanu
Nonlinear Dynamical Systems in Engineering Book PDF

Author : Vasile Marinca,Nicolae Herisanu
Publisher : Springer Science & Business Media
Page : 403 pages
File Size : 44,7 Mb
Release : 2012-01-05
Category : Technology & Engineering
ISBN : 9783642227356

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Nonlinear Dynamical Systems in Engineering by Vasile Marinca,Nicolae Herisanu Pdf

This book presents and extend different known methods to solve different types of strong nonlinearities encountered by engineering systems. A better knowledge of the classical methods presented in the first part lead to a better choice of the so-called “base functions”. These are absolutely necessary to obtain the auxiliary functions involved in the optimal approaches which are presented in the second part. Every chapter introduces a distinct approximate method applicable to nonlinear dynamical systems. Each approximate analytical approach is accompanied by representative examples related to nonlinear dynamical systems from to various fields of engineering.

Advances in the Homotopy Analysis Method

Shijun Liao
Advances in the Homotopy Analysis Method Book PDF

Author : Shijun Liao
Publisher : World Scientific
Page : 428 pages
File Size : 41,7 Mb
Release : 2013-11-26
Category : Mathematics
ISBN : 9789814551267

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Advances in the Homotopy Analysis Method by Shijun Liao Pdf

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. Contents:Chance and Challenge: A Brief Review of Homotopy Analysis Method (S-J Liao)Predictor Homotopy Analysis Method (PHAM) (S Abbasbandy and E Shivanian)Spectral Homotopy Analysis Method for Nonlinear Boundary Value Problems (S Motsa and P Sibanda)Stability of Auxiliary Linear Operator and Convergence-Control Parameter (R A Van Gorder)A Convergence Condition of the Homotopy Analysis Method (M Turkyilmazoglu)Homotopy Analysis Method for Some Boundary Layer Flows of Nanofluids (T Hayat and M Mustafa)Homotopy Analysis Method for Fractional Swift–Hohenberg Equation (S Das and K Vishal)HAM-Based Package NOPH for Periodic Oscillations of Nonlinear Dynamic Systems (Y-P Liu)HAM-Based Mathematica Package BVPh 2.0 for Nonlinear Boundary Value Problems (Y-L Zhao and S-J Liao) Readership: Graduate students and researchers in applied mathematics, physics, nonlinear mechanics, engineering and finance. Keywords:Analytic Approxiamtion Method;Nonlinear;Homotopy;Applied MathematicsKey Features:The method described in the book can overcome almost all restrictions of other analytic approximation method for nonlinear problemsThis book is the first in homotopy analysis method, covering the newest advances, contributed by many top experts in different fields

Homotopy-Based Methods in Water Engineering

Manotosh Kumbhakar,Vijay P. Singh
Homotopy Based Methods in Water Engineering Book PDF

Author : Manotosh Kumbhakar,Vijay P. Singh
Publisher : CRC Press
Page : 471 pages
File Size : 52,6 Mb
Release : 2023-07-20
Category : Technology & Engineering
ISBN : 9781000893359

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Homotopy-Based Methods in Water Engineering by Manotosh Kumbhakar,Vijay P. Singh Pdf

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

Beyond Perturbation

Shijun Liao
Beyond Perturbation Book PDF

Author : Shijun Liao
Publisher : CRC Press
Page : 335 pages
File Size : 48,5 Mb
Release : 2003-10-27
Category : Mathematics
ISBN : 9781135438296

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Beyond Perturbation by Shijun Liao Pdf

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.

New Numerical and Analytical Methods for Nonlinear Partial Differential Equations with Applications in Quantum Physics

Mustafa Inc,Xiao-Jun Yang,Devendra Kumar
New Numerical and Analytical Methods for Nonlinear Partial Differential Equations with Applications in Quantum Physics Book PDF

Author : Mustafa Inc,Xiao-Jun Yang,Devendra Kumar
Publisher : Frontiers Media SA
Page : 160 pages
File Size : 46,8 Mb
Release : 2023-11-20
Category : Science
ISBN : 9782832539439

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New Numerical and Analytical Methods for Nonlinear Partial Differential Equations with Applications in Quantum Physics by Mustafa Inc,Xiao-Jun Yang,Devendra Kumar Pdf

Various numerical and analytical methods have been used to investigate the models of real-world phenomena. Namely, real-world models from quantum physics have been investigated by many researchers. This Research Topic aims to promote and exchange new and important theoretical and numerical results to study the dynamics of complex physical systems. In particular, the Research Topic will focus on numerical and analytical methods for nonlinear partial differential equations which have applications for quantum physical systems. Authors are encouraged to introduce their latest original research articles. The Research Topic will cover, but is not limited to, the following themes: - Mathematical methods in physics - Representations of Lie groups in physics - Quantum fields - Advanced numerical methods and techniques for nonlinear partial differential equations - Schrödinger classical and fractional operators - Conservation laws

Optimal Auxiliary Functions Method for Nonlinear Dynamical Systems

Vasile Marinca,Nicolae Herisanu,Bogdan Marinca
Optimal Auxiliary Functions Method for Nonlinear Dynamical Systems Book PDF

Author : Vasile Marinca,Nicolae Herisanu,Bogdan Marinca
Publisher : Springer Nature
Page : 479 pages
File Size : 48,6 Mb
Release : 2021-07-14
Category : Technology & Engineering
ISBN : 9783030756536

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Optimal Auxiliary Functions Method for Nonlinear Dynamical Systems by Vasile Marinca,Nicolae Herisanu,Bogdan Marinca Pdf

This book presents the optimal auxiliary functions method and applies it to various engineering problems and in particular in boundary layer problems. The cornerstone of the presented procedure is the concept of “optimal auxiliary functions” which are needed to obtain accurate results in an efficient way. Unlike other known analytic approaches, this procedure provides us with a simple but rigorous way to control and adjust the convergence of the solutions of nonlinear dynamical systems. The optimal auxiliary functions are depending on some convergence-control parameters whose optimal values are rigorously determined from mathematical point of view. The capital strength of our procedure is its fast convergence, since after only one iteration, we obtain very accurate analytical solutions which are very easy to be verified. Moreover, no simplifying hypothesis or assumptions are made. The book contains a large amount of practical models from various fields of engineering such as classical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines, and many more. The book is a continuation of our previous books “Nonlinear Dynamical Systems in Engineering. Some Approximate Approaches”, Springer-2011 and “The Optimal Homotopy Asymptotic Method. Engineering Applications”, Springer-2015.

External Magnetic Field Effects on Hydrothermal Treatment of Nanofluid

Mohsen Sheikholeslami,Davood Domairry Ganji
External Magnetic Field Effects on Hydrothermal Treatment of Nanofluid Book PDF

Author : Mohsen Sheikholeslami,Davood Domairry Ganji
Publisher : William Andrew
Page : 354 pages
File Size : 48,8 Mb
Release : 2016-03-08
Category : Science
ISBN : 9780323431774

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External Magnetic Field Effects on Hydrothermal Treatment of Nanofluid by Mohsen Sheikholeslami,Davood Domairry Ganji Pdf

This book seeks to comprehensively cover recent progress in computational fluid dynamics and nonlinear science and its applications to MHD and FHD nanofluid flow and heat transfer. The book will be a valuable reference source to researchers in various fields, including materials science, nanotechnology, mathematics, physics, information science, engineering and medicine, seeing to understand the impact of external magnetic fields on the hydrothermal behavior of nanofluids in order to solve a wide variety of theoretical and practical problems. Readers will gain a full understanding of the fundamentals in new numerical and analytical methods in MHD (Magnetohydrodynamics) Includes complete coverage of governing equations in which nanofluid is used as working fluid, and where magnetic fields are applied to nanofluids A single-source reference covering recent progress in computational fluid dynamics and nonlinear science, and its applications to MHD and FHD nanofluid flow and heat transfer

Applications of Semi-Analytical Methods for Nanofluid Flow and Heat Transfer

Mohsen Sheikholeslami,Davood Domairry Ganji
Applications of Semi Analytical Methods for Nanofluid Flow and Heat Transfer Book PDF

Author : Mohsen Sheikholeslami,Davood Domairry Ganji
Publisher : Elsevier
Page : 888 pages
File Size : 40,5 Mb
Release : 2018-01-02
Category : Science
ISBN : 9780128136768

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Applications of Semi-Analytical Methods for Nanofluid Flow and Heat Transfer by Mohsen Sheikholeslami,Davood Domairry Ganji Pdf

Application of Semi-Analytical Methods for Nanofluid Flow and Heat Transfer applies semi-analytical methods to solve a range of engineering problems. After various methods are introduced, their application in nanofluid flow and heat transfer, magnetohydrodynamic flow, electrohydrodynamic flow and heat transfer, and nanofluid flow in porous media within several examples are explored. This is a valuable reference resource for materials scientists and engineers that will help familiarize them with a wide range of semi-analytical methods and how they are used in nanofluid flow and heat transfer. The book also includes case studies to illustrate how these methods are used in practice. Presents detailed information, giving readers a complete familiarity with governing equations where nanofluid is used as working fluid Provides the fundamentals of new analytical methods, applying them to applications of nanofluid flow and heat transfer in the presence of magnetic and electric field Gives a detailed overview of nanofluid motion in porous media

Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition

Anonim
Issues in Logic Operations and Computational Mathematics and Geometry 2011 Edition Book PDF

Author : Anonim
Publisher : ScholarlyEditions
Page : 995 pages
File Size : 41,7 Mb
Release : 2012-01-09
Category : Mathematics
ISBN : 9781464964794

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Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition by Anonim Pdf

Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Logic, Operations, and Computational Mathematics and Geometry. The editors have built Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Logic, Operations, and Computational Mathematics and Geometry in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Fractional Derivatives with Mittag-Leffler Kernel

José Francisco Gómez,Lizeth Torres,Ricardo Fabricio Escobar
Fractional Derivatives with Mittag Leffler Kernel Book PDF

Author : José Francisco Gómez,Lizeth Torres,Ricardo Fabricio Escobar
Publisher : Springer
Page : 341 pages
File Size : 40,9 Mb
Release : 2019-02-13
Category : Technology & Engineering
ISBN : 9783030116620

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Fractional Derivatives with Mittag-Leffler Kernel by José Francisco Gómez,Lizeth Torres,Ricardo Fabricio Escobar Pdf

This book offers a timely overview of fractional calculus applications, with a special emphasis on fractional derivatives with Mittag-Leffler kernel. The different contributions, written by applied mathematicians, physicists and engineers, offers a snapshot of recent research in the field, highlighting the current methodological frameworks together with applications in different fields of science and engineering, such as chemistry, mechanics, epidemiology and more. It is intended as a timely guide and source of inspiration for graduate students and researchers in the above-mentioned areas.

Computer Algebra in Scientific Computing

Vladimir P. Gerdt,Wolfram Koepf,Werner M. Seiler,Evgenii V. Vorozhtsov
Computer Algebra in Scientific Computing Book PDF

Author : Vladimir P. Gerdt,Wolfram Koepf,Werner M. Seiler,Evgenii V. Vorozhtsov
Publisher : Springer
Page : 494 pages
File Size : 48,9 Mb
Release : 2015-09-10
Category : Computers
ISBN : 9783319240213

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Computer Algebra in Scientific Computing by Vladimir P. Gerdt,Wolfram Koepf,Werner M. Seiler,Evgenii V. Vorozhtsov Pdf

This book constitutes the proceedings of the 17th International Workshop on Computer Algebra in Scientific Computing, CASC 2015, held in Aachen, Germany, in September 2015. The 35 full papers presented in this volume were carefully reviewed and selected from 42 submissions. They deal with the ongoing progress both in theoretical computer algebra and its expanding applications. New and closer interactions are fostered by combining the area of computer algebra methods and systems and the application of the tools of computer algebra for the solution of problems in scientific computing.