Title

Mathematical properties of h-curve in the frame work of the homotopy analysis method

Authors

Authors

S. Abbasbandy; E. Shivanian;K. Vajravelu

Comments

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Abbreviated Journal Title

Commun. Nonlinear Sci. Numer. Simul.

Keywords

Homotopy analysis method; Convergence-controller parameter; h-curve; Horizontal line; BOUNDARY-LAYER-FLOW; ANALYTIC SOLUTION; STRETCHING SHEET; HEAT-TRANSFER; AXISYMMETRICAL FLOW; EXPLICIT SOLUTION; 3RD-GRADE FLUID; 3RD-ORDER; FLUID; KDV EQUATION; SOLVE; Mathematics, Applied; Mathematics, Interdisciplinary Applications; Mechanics; Physics, Fluids & Plasmas; Physics, Mathematical

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 h-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. (C) 2011 Elsevier B.V. All rights reserved.

Journal Title

Communications in Nonlinear Science and Numerical Simulation

Volume

16

Issue/Number

11

Publication Date

1-1-2011

Document Type

Article

Language

English

First Page

4268

Last Page

4275

WOS Identifier

WOS:000292536900013

ISSN

1007-5704

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