LEADER 07162nam 22007695 450 001 9910299819503321 005 20250609112022.0 010 $a3-319-15374-9 024 7 $a10.1007/978-3-319-15374-2 035 $a(CKB)3710000000387652 035 $a(EBL)2094376 035 $a(SSID)ssj0001496800 035 $a(PQKBManifestationID)11945427 035 $a(PQKBTitleCode)TC0001496800 035 $a(PQKBWorkID)11490263 035 $a(PQKB)10487320 035 $a(DE-He213)978-3-319-15374-2 035 $a(MiAaPQ)EBC2094376 035 $a(PPN)185485316 035 $a(MiAaPQ)EBC3109243 035 $a(EXLCZ)993710000000387652 100 $a20150402d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe Optimal Homotopy Asymptotic Method $eEngineering Applications /$fby Vasile Marinca, Nicolae Herisanu 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (476 p.) 300 $aDescription based upon print version of record. 311 08$a3-319-15373-0 320 $aIncludes bibliographical references at the end of each chapters. 327 $aPreface; 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 327 $a3.3.1 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 327 $a4.1.4 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 327 $a4.5 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 327 $a4.8.2 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 Volterras? Population Model; 4.10.1 Numerical Examples; 4.11 Lotka-Volterra Model with Three Species; 4.11.1 Numerical Examples; 4.12 Bratus? Problem; 4.12.1 The Exact Solution of Bratus? Problem 4.548; 4.12.2 Solutions of the Bratus? Problem by Means of OHAM 327 $a4.12.3 Numerical Examples 330 $aThis 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. 606 $aMechanics 606 $aMechanics, Applied 606 $aComputer science$xMathematics 606 $aSociophysics 606 $aEconophysics 606 $aTheoretical and Applied Mechanics$3https://scigraph.springernature.com/ontologies/product-market-codes/T15001 606 $aComputational Mathematics and Numerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M1400X 606 $aData-driven Science, Modeling and Theory Building$3https://scigraph.springernature.com/ontologies/product-market-codes/P33030 615 0$aMechanics. 615 0$aMechanics, Applied. 615 0$aComputer science$xMathematics. 615 0$aSociophysics. 615 0$aEconophysics. 615 14$aTheoretical and Applied Mechanics. 615 24$aComputational Mathematics and Numerical Analysis. 615 24$aData-driven Science, Modeling and Theory Building. 676 $a518 676 $a620 676 $a620.1 676 $a621 700 $aMarinca$b Vasile$4aut$4http://id.loc.gov/vocabulary/relators/aut$0721166 702 $aHerisanu$b Nicolae$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910299819503321 996 $aThe Optimal Homotopy Asymptotic Method$92515633 997 $aUNINA