Control of error in the homotopy analysis of nonlinear Klein-Gordon initial value problems

    Authors

    M. Russo;R. A. Van Gorder

    Comments

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    Abbreviated Journal Title

    Appl. Math. Comput.

    Keywords

    Quasilinear Klein-Gordon equation; sinh-Gordon equation; tanh-Gordon; equation; Homotopy analysis method; Control of error; EMDEN-FOWLER TYPE; SINH-GORDON; ASYMPTOTIC METHOD; EXPANSION METHOD; EQUATIONS; FLOW; EVOLUTION; FLUID; WAVES; Mathematics, Applied

    Abstract

    In the present paper, we discuss the application of homotopy analysis to general nonlinear Klein-Gordon type equations. We first outline the method for general forms of the nonlinearity, as well as for general functional forms of the initial conditions. In particular, we discuss a method of controlling the residual error in approximate solutions which may be found via homotopy analysis, through adequate selection of the convergence control parameter. With the general problem outlined, we apply the method to various equations, including the quasilinear cubic Klein-Gordon equation, the modified Liouville equation, the sinh-Gordon equation, and the tanh-Gordon equation. For each of these equations and related initial data, we obtain residual error minimizing solutions which demonstrate the qualitative behavior of the true solutions in each case. (C) 2012 Elsevier Inc. All rights reserved.

    Journal Title

    Applied Mathematics and Computation

    Volume

    219

    Issue/Number

    12

    Publication Date

    1-1-2013

    Document Type

    Article

    Language

    English

    First Page

    6494

    Last Page

    6509

    WOS Identifier

    WOS:000315708700013

    ISSN

    0096-3003

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