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Homotopy Analysis Method in Nonlinear Differential Equations / by Shijun Liao
版 | 1st ed. 2012. |
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出版者 | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
出版年 | 2012 |
大きさ | X, 400 p. 50 illus : online resource |
著者標目 | *Liao, Shijun author SpringerLink (Online service) |
件 名 | LCSH:Differential equations LCSH:Nonlinear Optics LCSH:Engineering mathematics LCSH:Engineering—Data processing FREE:Differential Equations FREE:Nonlinear Optics FREE:Mathematical and Computational Engineering Applications |
一般注記 | Basic Ideas -- Systematic Descriptions -- Advanced Approaches -- Convergent Series For Divergent Taylor Series -- Nonlinear Initial Value Problems -- Nonlinear Eigenvalue Problems -- Nonlinear Problems In Heat Transfer -- Nonlinear Problems With Free Or Moving Boundary -- Steady-State Similarity Boundary-Layer Flows -- Unsteady Similarity Boundary-Layer Flows -- Non-Similarity Boundary-Layer Flows -- Applications In Numerical Methods "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. HTTP:URL=https://doi.org/10.1007/978-3-642-25132-0 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9783642251320 |
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電子リソース |
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EB00208189 |
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※2017年9月4日以降