Systematic Descriptions and Related Theorems

Shijun Liao ()
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Shijun Liao: Shanghai Jiao Tong University

Chapter Chapter 4 in Homotopy Analysis Method in Nonlinear Differential Equations, 2012, pp 131-187 from Springer

Abstract: 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.

Keywords: Homotopy Analysis Method; Conver Gence; Relate Theorem; Accor Ding; Order Deformation Equation (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-25132-0_4

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DOI: 10.1007/978-3-642-25132-0_4

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