# Homotopy Analysis Method in Nonlinear Differential Equations

• ShijunÂ Liao
Book

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 15-94
4. Shijun Liao
Pages 95-129
5. Shijun Liao
Pages 131-187
6. Shijun Liao
Pages 189-221
7. 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 285-314
4. Shijun Liao
Pages 315-361
5. Shijun Liao
Pages 363-381
6. Shijun Liao
Pages 383-401
7. Shijun Liao
Pages 403-421
4. ### Applications in Nonlinear Partial Differential Equations

1. Front Matter
Pages 423-423
2. Shijun Liao
Pages 425-459
3. Shijun Liao
Pages 461-491
4. Shijun Liao
Pages 493-522
5. Shijun Liao
Pages 523-562
5. Back Matter
Pages 563-565

### 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

• ShijunÂ 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
• Buy this book on publisher's site