LEADER 04164oam 2200457 450 001 9910807275303321 005 20190911112729.0 010 $a981-4551-25-2 035 $a(OCoLC)869281856 035 $a(MiFhGG)GVRL8RBR 035 $a(EXLCZ)992550000001191468 100 $a20130716h20142014 uy 0 101 0 $aeng 135 $aurun|---uuuua 181 $ctxt 182 $cc 183 $acr 200 00$aAdvances in the homotopy analysis method /$feditor, Shijun Liao, Shanghai Jiao Tong University, China 210 1$aNew Jersey :$cWorld Scientific,$d[2014] 210 4$d?2014 215 $a1 online resource (viii, 417 pages) $cillustrations 225 0 $aGale eBooks 300 $aDescription based upon print version of record. 311 $a981-4551-24-4 311 $a1-306-39640-9 320 $aIncludes bibliographical references. 327 $aPreface; Contents; 1. Chance and Challenge: A Brief Review of Homotopy Analysis Method; 1.1. Background; 1.2. A brief history of the HAM; 1.3. Some advances of the HAM; 1.3.1. Generalized zeroth-order deformation equation; 1.3.2. Spectral HAM and complicated auxiliary operator; 1.3.3. Predictor HAM and multiple solutions; 1.3.4. Convergence condition and HAM-based software; 1.4. Relationships to other methods; 1.5. Chance and challenge: some suggested problems; 1.5.1. Periodic solutions of chaotic dynamic systems; 1.5.2. Periodic orbits of Newtonian three-body problem 327 $a1.5.3. Viscous flow past a sphere1.5.4. Viscous flow past a cylinder; 1.5.5. Nonlinear water waves; Acknowledgment; References; 2. Predictor Homotopy Analysis Method (PHAM); 2.1. Preliminaries; 2.2. Description of the method; 2.2.1. Zeroth-order deformation equation; 2.2.2. High-order deformation equation; 2.2.3. Prediction of the multiple solutions; 2.3. Convergence analysis; 2.4. Some illustrative models; 2.4.1. Nonlinear problem arising in heat transfer; 2.4.1.1. Model and exact solutions; 2.4.1.2. Prediction of dual solutions by the rule of multiplicity of solutions 327 $a2.4.1.3. Effective calculation of the two branches of solution2.4.2. Strongly nonlinear Bratu's equation; 2.4.2.1. Problem and exact solutions; 2.4.2.2. Prediction of multiple solutions by the rule of multiplicity of solutions; 2.4.2.3. Effective calculation of the two branches of solution; 2.4.3. Nonlinear reaction-diffusion model; 2.4.3.1. Equation and exact solutions; 2.4.3.2. Prediction of multiple solutions by the rule of multiplicity of solutions; 2.4.3.3. Calculation of the two branches of solution; 2.4.4. Mixed convection flows in a vertical channel 327 $a2.4.4.1. Prediction of dual solutions by the rule of multiplicity of solutions2.4.4.2. Effective calculation of the two branches of solution; 2.4.4.3. Further results; 2.5. Concluding remarks; References; 3. Spectral Homotopy Analysis Method for Nonlinear Boundary Value Problems; 3.1. Introduction; 3.2. Basic ideas of the spectral homotopy analysis method; 3.3. Some applications of the spectral homotopy analysis method; 3.3.1. Falkner-Skan boundary layer flow; 3.3.2. Eigenvalue problems; 3.3.3. Boundary value problems with multiple solutions; 3.3.4. Coupled nonlinear boundary value equations 330 $aUnlike 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 adva 606 $aHomotopy theory 615 0$aHomotopy theory. 676 $a514/.24 702 $aLiao$b Shijun$f1963- 801 0$bMiFhGG 801 1$bMiFhGG 906 $aBOOK 912 $a9910807275303321 996 $aAdvances in the homotopy analysis method$93932876 997 $aUNINA