Optimal Homotopy Analysis Method

Shijun Liao ()
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Shijun Liao: Shanghai Jiao Tong University

Chapter Chapter 3 in Homotopy Analysis Method in Nonlinear Differential Equations, 2012, pp 95-129 from Springer

Abstract: Abstract In this chapter, we describe and compare the different optimal approaches of the homotopy analysis method (HAM). A generalized optimal HAM is proposed, which logically contains the basic optimal HAM with only one convergence-control parameter and also the optimal HAM with an infinite number of parameters. It is found that approximations given by the optimal HAMs converge fast in general. Especially, the basic optimal HAM mostly gives good enough approximations. Thus, the optimal HAMs with a couple of convergence-control parameters are strongly suggested in practice.

Keywords: Homotopy Analysis Method; Pertur Bation; Auxiliary Linear Operator; Linear ODEs; Illustrative Descri Ption (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_3

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DOI: 10.1007/978-3-642-25132-0_3

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