1.

Record Nr.

UNINA9910807275303321

Titolo

Advances in the homotopy analysis method / / editor, Shijun Liao, Shanghai Jiao Tong University, China

Pubbl/distr/stampa

New Jersey : , : World Scientific, , [2014]

�2014

ISBN

981-4551-25-2

Descrizione fisica

1 online resource (viii, 417 pages) : illustrations

Collana

Gale eBooks

Disciplina

514/.24

Soggetti

Homotopy theory

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

Includes bibliographical references.

Nota di contenuto

Preface; 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

1.5.3. 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

2.4.1.3. 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

2.4.4.1. 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

Sommario/riassunto

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 adva