Liao edits this research volume on applications of the homotopy analysis method (HAM) in nonlinear problems, particularly where other common approaches such as perturbation methods may not be appropriate. The first chapter reviews the method, its mathematical basis, and describes its advantages. The book then goes into predictor HAM and spectral HAM, characterizes the stability of the method given variation of the linear operator and convergence-control parameters, and carefully assesses the convergence conditions of the method. Applications to boundary layer flows of nanofluids and the fractional Swift-Hohenberg equation follow. The final two contributions present packages for Maple and Mathematica utilizing HAM for periodic oscillations and nonlinear boundary value problems, respectively. Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)
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.
