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Systematic Descriptions and Related Theorems

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Homotopy Analysis Method in Nonlinear Differential Equations

Abstract

In this chapter, the homotopy analysis method (HAM) is systematically described in details as a whole. Mathematical theorems related to the so-called homotopy-derivative operator and deformation equations are proved, which are helpful to gain high-order approximations. Some theorems of convergence are proved, and the methods to control and accelerate convergence are generally described. A few of open questions are discussed.

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Authors and Affiliations

  1. Shanghai Jiao Tong University, Shanghai, 200030, China

    Shijun Liao

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  1. Shijun Liao
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© 2012 Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg

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Liao, S. (2012). Systematic Descriptions and Related Theorems. In: Homotopy Analysis Method in Nonlinear Differential Equations. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25132-0_4

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