vbid/9783642251320

Description

“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 Jiao Tong University, is a pioneer of the HAM.�Typham this is the title: Homotopy Analysis Method in Nonlinear Differential Equations