Homotopy
Analysis Method in Nonlinear Differential Equations
Shijun
LIAO
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.
Preface Content Basic Ideas
& Brief History of the HAM Examples BVPh APOh Free-downloaded codes