Title

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

Authors

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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