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

    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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