Overview
- Develops a powerful analytic method for strongly nonlinear differential equations
- Offers the latest theoretical developments of the method
- Demonstrates various novel, interesting applications in science, engineering and finance
- Includes free symbolic computation codes for easy understanding and use
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Table of contents (16 chapters)
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Front Matter
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Mathematica Package BVPh and Its Applications
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Front Matter
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Applications in Nonlinear Partial Differential Equations
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Front Matter
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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
- partial differential equations
- ordinary differential equations
About this book
"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. Â
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.Â
Authors and Affiliations
Bibliographic Information
Book Title: Homotopy Analysis Method in Nonlinear Differential Equations
Authors: Shijun Liao
DOI: https://doi.org/10.1007/978-3-642-25132-0
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Higher Education Press,Beijng and Springer-Verlag GmbH Berlin Heidelberg 2012
eBook ISBN: 978-3-642-25132-0Published: 22 June 2012
Edition Number: 1
Number of Pages: X, 400
Number of Illustrations: 50 b/w illustrations
Additional Information: Jointly published with Higher Education Press
Topics: Partial Differential Equations, Applications of Nonlinear Dynamics and Chaos Theory, Mathematical and Computational Engineering, Ordinary Differential Equations