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Optimal Homotopy Analysis Method

In: Homotopy Analysis Method in Nonlinear Differential Equations

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  • Shijun Liao

    (Shanghai Jiao Tong University)

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.

Suggested Citation

  • Shijun Liao, 2012. "Optimal Homotopy Analysis Method," Springer Books, in: Homotopy Analysis Method in Nonlinear Differential Equations, chapter 0, pages 95-129, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-25132-0_3
    DOI: 10.1007/978-3-642-25132-0_3
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