The Optimal Homotopy Asymptotic Method [electronic resource] : Engineering Applications /
Marinca, Vasile.author.
Herisanu, Nicolae.author.
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.
Description based upon print version of record.
Preface; Contents; Chapter 1: Introduction; References; Chapter 2: Optimal Homotopy Asymptotic Method; 2.1 A Short History of the Homotopy; 2.2 Basic Idea of OHAM; 2.3 Convergence of the Homotopy-Series 2.28; 2.4 Convergence of the Approximate Solution of Order m Given by Eq.2.29; References; Chapter 3: The First Alternative of the Optimal Homotopy Asymptotic Method; 3.1 Thin Film Flow of a Fourth-Grade Fluid Down a Vertical Cylinder; 3.1.1 Numerical Examples; 3.2 The Jeffery-Hamel Flow Problem; 3.2.1 Numerical Examples; 3.3 Oscillations of a Mass Attached to a Stretched Wire
3.3.1 Numerical Examples3.4 The Motion of a Particle on a Rotating Parabola; 3.4.1 Numerical Examples; 3.5 Nonlinear Oscillator with Discontinuities and Fractional-Power Restoring Force; References; Chapter 4: The Second Alternative of the Optimal Homotopy Asymptotic Method; 4.1 The Flow of a Walters-Type B ́Viscoelastic Fluid in a Vertical Channel with Porous Wall; 4.1.1 Problem Statement and Governing Equation; 4.1.2 Solution of Walters-Type B ́Viscoelastic Fluid in a Vertical Channel with OHAM; 4.1.3 Governing Equation of the Temperature and Its Solution
4.1.4 Numerical Results and Discussions4.2 Thin Film Flow of an Oldroyd 6-Constant Fluid over Moving Belt; 4.2.1 Governing Equations; 4.2.2 Application of OHAM to Thin Film Flow of an Oldroyd 6-Constant Fluid; 4.2.3 Numerical Results and Discussions; 4.3 Falkner-Skan Equation; 4.3.1 The Governing Equation; 4.3.2 Application of OHAM to Falkner-Skan Equation; 4.3.3 Numerical Examples; 4.4 Viscous Flow Due to a Stretching Surface with Partial Slip; 4.4.1 Equation of Motion; 4.4.2 Application of OHAM to Viscous Fluid Given by Eq.4.220; 4.4.3 Numerical Examples
4.5 The Flow and Heat Transfer in a Viscous Fluid Over an Unsteady Stretching Surface4.5.1 Equations of Motion; 4.5.2 Application of OHAM to Flow and Heat Transfer; 4.5.3 Numerical Examples; 4.6 Blasius ́Problem; 4.6.1 Solution of Blasius ́Problem by Optimal Homotopy Asymptotic Method; 4.7 Thermal Radiation on MHD Flow over a Stretching Porous Sheet; 4.7.1 Solution of the Problem with Optimal Homotopy Asymptotic Method; 4.7.2 Numerical Examples; 4.8 Nonlinear Equations Arising in Heat Transfer; 4.8.1 Cooling of a Lumped System with Variable Specific Heat; 4.8.1.1 Numerical Examples
4.8.2 The Temperature Distribution Equation in a Thick Rectangular Fin Radiation to Free Space4.8.2.1 Numerical Examples; 4.8.3 A Heat Transfer Problem; 4.8.3.1 Numerical Examples; 4.9 The Nonlinear Age-Structured Population Models; 4.9.1 Analytical Solution for Nonlinear Age-Structured Population Models Using OHAM; 4.10 Volterraś Population Model; 4.10.1 Numerical Examples; 4.11 Lotka-Volterra Model with Three Species; 4.11.1 Numerical Examples; 4.12 Bratuś Problem; 4.12.1 The Exact Solution of Bratuś Problem 4.548; 4.12.2 Solutions of the Bratuś Problem by Means of OHAM
4.12.3 Numerical Examples
Includes bibliographical references at the end of each chapters.
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.
Mechanics.
Mechanics, Applied.
Computer mathematics.
Sociophysics.
Econophysics.
Theoretical and Applied Mechanics.
Computational Mathematics and Numerical Analysis.
Data-driven Science, Modeling and Theory Building.