On the selection of auxiliary functions, operators, and convergence control parameters in the application of the Homotopy Analysis Method to nonlinear differential equations: A general approach

    Authors

    R. A. Van Gorder;K. Vajravelu

    Comments

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    Abbreviated Journal Title

    Commun. Nonlinear Sci. Numer. Simul.

    Keywords

    Homotopy Analysis Method; Nonlinear differential equations; Series; solutions; Perturbation methods; ANALYTIC SOLUTION; KDV EQUATION; SOLITON-SOLUTIONS; SERIES SOLUTIONS; GRADE FLUID; FLOW; SOLVE; SYSTEM; FILM; Mathematics, Applied; Mathematics, Interdisciplinary Applications; Mechanics; Physics, Fluids & Plasmas; Physics, Mathematical

    Abstract

    The Homotopy Analysis Method of Liao [Liao SJ. Beyond perturbation: introduction to the Homotopy Analysis Method. Boca Raton: Chapman & Hall/CRC Press; 20031 has proven useful in obtaining analytical solutions to various nonlinear differential equations. In this method, one has great freedom to select auxiliary functions, operators, and parameters in order to ensure the convergence of the approximate solutions and to increase both the rate and region of convergence. We discuss in this paper the selection of the initial approximation, auxiliary linear operator, auxiliary function, and convergence control parameter in the application of the Homotopy Analysis Method, in a fairly general setting. Further, we discuss various convergence requirements on solutions. (C) 2009 Elsevier B.V. All rights reserved.

    Journal Title

    Communications in Nonlinear Science and Numerical Simulation

    Volume

    14

    Issue/Number

    12

    Publication Date

    1-1-2009

    Document Type

    Article

    Language

    English

    First Page

    4078

    Last Page

    4089

    WOS Identifier

    WOS:000267589600006

    ISSN

    1007-5704

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