Homotopy Analysis Method in Nonlinear Differential Equations

  • Shijun Liao

Table of contents

  1. Front Matter
    Pages i-xv
  2. Basic Ideas and Theorems

    1. Front Matter
      Pages 1-1
    2. Shijun Liao
      Pages 3-14
    3. Shijun Liao
      Pages 95-129
    4. Shijun Liao
      Pages 189-221
    5. Shijun Liao
      Pages 223-235
  3. Mathematica Package BVPh and Its Applications

    1. Front Matter
      Pages 237-237
    2. Shijun Liao
      Pages 239-284
    3. Shijun Liao
      Pages 383-401
    4. Shijun Liao
      Pages 403-421
  4. Applications in Nonlinear Partial Differential Equations

About this book

Introduction

"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. 

 

Keywords

Analytic approximation Analytic approximation Analytic approximation Differential equations Differential equations Differential equations Homotopy analysis method Homotopy analysis method Homotopy analysis method Series solution Series solution Series solution Strong nonlinearity Strong nonlinearity Strong nonlinearity

Authors and affiliations

  • Shijun Liao
    • 1
  1. 1.Shanghai Jiao Tong UniversityShanghaiChina

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-25132-0
  • Copyright Information Higher Education Press,Beijng and Springer-Verlag GmbH Berlin Heidelberg 2012
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-25131-3
  • Online ISBN 978-3-642-25132-0
  • About this book