Nonlinear Flow Phenomena And Homotopy Analysis

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Nonlinear Flow Phenomena and Homotopy Analysis

Kuppalapalle Vajravelu,Robert A. Van Gorder
Nonlinear Flow Phenomena and Homotopy Analysis Book PDF

Author : Kuppalapalle Vajravelu,Robert A. Van Gorder
Publisher : Springer Science & Business Media
Page : 197 pages
File Size : 49,6 Mb
Release : 2013-07-22
Category : Mathematics
ISBN : 9783642321023

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Nonlinear Flow Phenomena and Homotopy Analysis by Kuppalapalle Vajravelu,Robert A. Van Gorder Pdf

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.

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 : 41,6 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

Beyond Perturbation

Shijun Liao
Beyond Perturbation Book PDF

Author : Shijun Liao
Publisher : CRC Press
Page : 335 pages
File Size : 54,8 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.

Mathematical Modeling, Computational Intelligence Techniques and Renewable Energy

Manoj Sahni,José M. Merigó,Walayat Hussain,Ernesto León-Castro,Raj Kumar Verma,Ritu Sahni
Mathematical Modeling Computational Intelligence Techniques and Renewable Energy Book PDF

Author : Manoj Sahni,José M. Merigó,Walayat Hussain,Ernesto León-Castro,Raj Kumar Verma,Ritu Sahni
Publisher : Springer Nature
Page : 474 pages
File Size : 50,6 Mb
Release : 2023-05-08
Category : Technology & Engineering
ISBN : 9789811999062

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Mathematical Modeling, Computational Intelligence Techniques and Renewable Energy by Manoj Sahni,José M. Merigó,Walayat Hussain,Ernesto León-Castro,Raj Kumar Verma,Ritu Sahni Pdf

The book is a collection of best selected research papers presented at the Third International Conference on “Mathematical Modeling, Computational Intelligence Techniques and Renewable Energy (MMCITRE 2022),” organized by the University of Technology Sydney, Australia, in association with the Department of Mathematics, Pandit Deendayal Energy University, India, and Forum for Interdisciplinary Mathematics. This book presents new knowledge and recent developments in all aspects of computational techniques, mathematical modeling, energy systems, applications of fuzzy sets and intelligent computing. The book provides innovative works of researchers, academicians and students in the area of interdisciplinary mathematics, statistics, computational intelligence and renewable energy.

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 : 50,6 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

Fluid Flow, Heat and Mass Transfer at Bodies of Different Shapes

Kuppalapalle Vajravelu,Swati Mukhopadhyay
Fluid Flow Heat and Mass Transfer at Bodies of Different Shapes Book PDF

Author : Kuppalapalle Vajravelu,Swati Mukhopadhyay
Publisher : Academic Press
Page : 202 pages
File Size : 43,7 Mb
Release : 2015-09-08
Category : Mathematics
ISBN : 9780128037850

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Fluid Flow, Heat and Mass Transfer at Bodies of Different Shapes by Kuppalapalle Vajravelu,Swati Mukhopadhyay Pdf

Most of the equations governing the problems related to science and engineering are nonlinear in nature. As a result, they are inherently difficult to solve. Analytical solutions are available only for some special cases. For other cases, one has no easy means but to solve the problem must depend on numerical solutions. Fluid Flow, Heat and Mass Transfer at Bodies of Different Shapes: Numerical Solutions presents the current theoretical developments of boundary layer theory, a branch of transport phenomena. Also, the book addresses the theoretical developments in the area and presents a number of physical problems that have been solved by analytical or numerical method. It is focused particularly on fluid flow problems governed by nonlinear differential equations. The book is intended for researchers in applied mathematics, physics, mechanics and engineering. Addresses basic concepts to understand the theoretical framework for the method Provides examples of nonlinear problems that have been solved through the use of numerical method Focuses on fluid flow problems governed by nonlinear equations

The Optimal Homotopy Asymptotic Method

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

Author : Vasile Marinca,Nicolae Herisanu
Publisher : Springer
Page : 465 pages
File Size : 43,8 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.

Analysis, Geometry, Nonlinear Optimization And Applications

Panos M Pardalos,Themistocles M Rassias
Analysis Geometry Nonlinear Optimization And Applications Book PDF

Author : Panos M Pardalos,Themistocles M Rassias
Publisher : World Scientific
Page : 895 pages
File Size : 50,9 Mb
Release : 2023-03-20
Category : Mathematics
ISBN : 9789811261589

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Analysis, Geometry, Nonlinear Optimization And Applications by Panos M Pardalos,Themistocles M Rassias Pdf

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 Solutions of Realistic Nonlinear Phenomena

J. A. Tenreiro Machado,Necati Özdemir,Dumitru Baleanu
Numerical Solutions of Realistic Nonlinear Phenomena Book PDF

Author : J. A. Tenreiro Machado,Necati Özdemir,Dumitru Baleanu
Publisher : Springer Nature
Page : 231 pages
File Size : 40,5 Mb
Release : 2020-02-19
Category : Mathematics
ISBN : 9783030371418

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Numerical Solutions of Realistic Nonlinear Phenomena by J. A. Tenreiro Machado,Necati Özdemir,Dumitru Baleanu Pdf

This collection covers new aspects of numerical methods in applied mathematics, engineering, and health sciences. It provides recent theoretical developments and new techniques based on optimization theory, partial differential equations (PDEs), mathematical modeling and fractional calculus that can be used to model and understand complex behavior in natural phenomena. Specific topics covered in detail include new numerical methods for nonlinear partial differential equations, global optimization, unconstrained optimization, detection of HIV- Protease, modelling with new fractional operators, analysis of biological models, and stochastic modelling.

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 : 52,7 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.

Proceedings of the Second International Conference on Soft Computing for Problem Solving (SocProS 2012), December 28-30, 2012

B. V. Babu,Atulya Nagar,Kusum Deep,Millie Pant,Jagdish Chand Bansal,Kanad Ray,Umesh Gupta
Proceedings of the Second International Conference on Soft Computing for Problem Solving SocProS 2012 December 28 30 2012 Book PDF

Author : B. V. Babu,Atulya Nagar,Kusum Deep,Millie Pant,Jagdish Chand Bansal,Kanad Ray,Umesh Gupta
Publisher : Springer
Page : 1604 pages
File Size : 42,5 Mb
Release : 2014-07-08
Category : Technology & Engineering
ISBN : 9788132216025

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Proceedings of the Second International Conference on Soft Computing for Problem Solving (SocProS 2012), December 28-30, 2012 by B. V. Babu,Atulya Nagar,Kusum Deep,Millie Pant,Jagdish Chand Bansal,Kanad Ray,Umesh Gupta Pdf

The present book is based on the research papers presented in the International Conference on Soft Computing for Problem Solving (SocProS 2012), held at JK Lakshmipat University, Jaipur, India. This book provides the latest developments in the area of soft computing and covers a variety of topics, including mathematical modeling, image processing, optimization, swarm intelligence, evolutionary algorithms, fuzzy logic, neural networks, forecasting, data mining, etc. The objective of the book is to familiarize the reader with the latest scientific developments that are taking place in various fields and the latest sophisticated problem solving tools that are being developed to deal with the complex and intricate problems that are otherwise difficult to solve by the usual and traditional methods. The book is directed to the researchers and scientists engaged in various fields of Science and Technology.

Mathematical Modelling, Applied Analysis and Computation

Jagdev Singh,Devendra Kumar,Hemen Dutta,Dumitru Baleanu,Sunil Dutt Purohit
Mathematical Modelling Applied Analysis and Computation Book PDF

Author : Jagdev Singh,Devendra Kumar,Hemen Dutta,Dumitru Baleanu,Sunil Dutt Purohit
Publisher : Springer Nature
Page : 311 pages
File Size : 43,7 Mb
Release : 2019-08-31
Category : Mathematics
ISBN : 9789811396083

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Mathematical Modelling, Applied Analysis and Computation by Jagdev Singh,Devendra Kumar,Hemen Dutta,Dumitru Baleanu,Sunil Dutt Purohit Pdf

This book contains original research papers presented at the International Conference on Mathematical Modelling, Applied Analysis and Computation, held at JECRC University, Jaipur, India, on 6-8 July, 2018. Organized into 20 chapters, the book focuses on theoretical and applied aspects of various types of mathematical modelling such as equations of various types, fuzzy mathematical models, automata, Petri nets and bond graphs for systems of dynamic nature and the usage of numerical techniques in handling modern problems of science, engineering and finance. It covers the applications of mathematical modelling in physics, chemistry, biology, mechanical engineering, civil engineering, computer science, social science and finance. A wide variety of dynamical systems like deterministic, stochastic, continuous, discrete or hybrid, with respect to time, are discussed in the book. It provides the mathematical modelling of various problems arising in science and engineering, and also new efficient numerical approaches for solving linear and nonlinear problems and rigorous mathematical theories, which can be used to analyze a different kind of mathematical models. The conference was aimed at fostering cooperation among students and researchers in areas of applied analysis, engineering and computation with the deliberations to inculcate new research ideas in their relevant fields. This volume will provide a comprehensive introduction to recent theories and applications of mathematical modelling and numerical simulation, which will be a valuable resource for graduate students and researchers of mathematical modelling and industrial mathematics.

Modeling and Analysis of Modern Fluid Problems

Liancun Zheng,Xinxin Zhang
Modeling and Analysis of Modern Fluid Problems Book PDF

Author : Liancun Zheng,Xinxin Zhang
Publisher : Academic Press
Page : 480 pages
File Size : 55,6 Mb
Release : 2017-04-26
Category : Science
ISBN : 9780128117590

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Modeling and Analysis of Modern Fluid Problems by Liancun Zheng,Xinxin Zhang Pdf

Modeling and Analysis of Modern Fluids helps researchers solve physical problems observed in fluid dynamics and related fields, such as heat and mass transfer, boundary layer phenomena, and numerical heat transfer. These problems are characterized by nonlinearity and large system dimensionality, and ‘exact’ solutions are impossible to provide using the conventional mixture of theoretical and analytical analysis with purely numerical methods. To solve these complex problems, this work provides a toolkit of established and novel methods drawn from the literature across nonlinear approximation theory. It covers Padé approximation theory, embedded-parameters perturbation, Adomian decomposition, homotopy analysis, modified differential transformation, fractal theory, fractional calculus, fractional differential equations, as well as classical numerical techniques for solving nonlinear partial differential equations. In addition, 3D modeling and analysis are also covered in-depth. Systematically describes powerful approximation methods to solve nonlinear equations in fluid problems Includes novel developments in fractional order differential equations with fractal theory applied to fluids Features new methods, including Homotypy Approximation, embedded-parameter perturbation, and 3D models and analysis

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 : 54,6 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.

Nonlinear Dynamics and Applications

Santo Banerjee,Asit Saha
Nonlinear Dynamics and Applications Book PDF

Author : Santo Banerjee,Asit Saha
Publisher : Springer Nature
Page : 1433 pages
File Size : 44,7 Mb
Release : 2022-10-06
Category : Science
ISBN : 9783030997922

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Nonlinear Dynamics and Applications by Santo Banerjee,Asit Saha Pdf

This book covers recent trends and applications of nonlinear dynamics in various branches of society, science, and engineering. The selected peer-reviewed contributions were presented at the International Conference on Nonlinear Dynamics and Applications (ICNDA 2022) at Sikkim Manipal Institute of Technology (SMIT) and cover a broad swath of topics ranging from chaos theory and fractals to quantum systems and the dynamics of the COVID-19 pandemic. Organized by the SMIT Department of Mathematics, this international conference offers an interdisciplinary stage for scientists, researchers, and inventors to present and discuss the latest innovations and trends in all possible areas of nonlinear dynamics.