Basic Ideas -- Systematic Descriptions -- Advanced Approaches -- Convergent Series For Divergent Taylor Series -- Nonlinear Initial Value Problems -- Nonlinear Eigenvalue Problems -- Nonlinear Problems In Heat Transfer -- Nonlinear Problems With Free Or Moving Boundary -- Steady-State Similarity Boundary-Layer Flows -- Unsteady Similarity Boundary-Layer Flows -- Non-Similarity Boundary-Layer Flows -- Applications In Numerical Methods.

"Homotopy Analysis Method in Nonlinear Differential Equations" presents the latest developments and applications of the analytic approximation method for highly nonlinear problems, namely the homotopy analysis method (HAM).  Unlike perturbation methods, the HAM has nothing to do with small/large physical parameters.  In addition, it provides great freedom to choose the equation-type of linear sub-problems and the base functions of a solution.  Above all, it provides a convenient way to guarantee the convergence of a solution. This book consists of three parts.  Part I provides its basic ideas and theoretical development.  Part II presents the HAM-based Mathematica package BVPh 1.0 for nonlinear boundary-value problems and its applications.  Part III shows the validity of the HAM for nonlinear PDEs, such as the American put option and resonance criterion of nonlinear travelling waves.  New solutions to a number of nonlinear problems are presented, illustrating the originality of the HAM.  Mathematica codes are freely available online to make it easy for readers to understand and use the HAM.    This book is suitable for researchers and postgraduates in applied mathematics, physics, nonlinear mechanics, finance and engineering. Dr. Shijun Liao, a distinguished professor of Shanghai Jiaotong University, is a pioneer of the HAM.