Title

Mathematical Properties Of ℏ-Curve In The Frame Work Of The Homotopy Analysis Method

Keywords

ℏ-Curve; Convergence-controller parameter; Homotopy analysis method; Horizontal line

Abstract

As it is described in the frame work of the homotopy analysis method (HAM), the convergence-control parameter is the main auxiliary tool which distinguishes this method form the other analytical methods. Moreover the convergence is usually obtained by the so-called ℏ-curve which possesses horizontal line property. The purpose of this paper is to answer this fundamental question: That is, why the horizontal line occurs in the plot of HAM series solution at some points corresponding to the convergence-control parameter. Also, the mathematical proof and the properties of this main issue are presented. Furthermore, some illustrative examples are presented and the salient features are discussed. © 2011 Elsevier B.V.

Publication Date

11-1-2011

Publication Title

Communications in Nonlinear Science and Numerical Simulation

Volume

16

Issue

11

Number of Pages

4268-4275

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.cnsns.2011.03.031

Socpus ID

79957919455 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/79957919455

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