"Homotopy theory." . . "Appl. Mathematics/Computational Methods of Engineering." . . "Appl.Mathematics/Computational Methods of Engineering." . "Homotopie" . . "Homotopie." . "Approximation" . . "Approximation." . "Ordinary Differential Equations." . . "Équations différentielles non linéaires." . . "Differential equations, Partial." . . "Mathematics." . . "Partial Differential Equations." . . "Differential equations, Nonlinear." . . "Differential equations." . . . "Electronic books" . "Electronic books"@en . . . . . . . . . . . . . . . . . . . . . . . . "Homotopy analysis method in nonlinear differential equations" . "Homotopy analysis method in nonlinear differential equations"@en . . . . . . "Homotopy Analysis Method in Nonlinear Differential Equations" . "Homotopy Analysis Method in Nonlinear Differential Equations"@en . . "\"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.℗¡ ℗¡" . . . . . . . . . . . . . . . . . . . . . . . . "Mathematical analysis." . . . . "Nichtlineare Differentialgleichung" . . "Nichtlineare Differentialgleichung." . "Nonlinear Dynamics." . . "Engineering mathematics." . . "Analyse mathématique." . . "MATHEMATICS / Differential Equations / General" . .