Similarity solutions of the boundary layer equations for a nonlinearly stretching sheet

Journal article

Authors/Editors

Siginer, Dennis

Research Areas

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Publication Details

Author list: Akyildiz FT, Siginer DA, Vajravelu K, Cannon JR, Van Gorder RA

Publisher: Wiley

Place: HOBOKEN

Publication year: 2010

Journal: Mathematical Methods in the Applied Sciences (0170-4214)

Journal acronym: MATH METHOD APPL SCI

Volume number: 33

Issue number: 5

Start page: 601

End page: 606

Number of pages: 6

ISSN: 0170-4214

eISSN: 1099-1476

Languages: English-Great Britain (EN-GB)

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Abstract

Consideration is given to a class of nonlinear third-order differential equations arising in fluid flow over a nonlinearly stretching sheet. Existence of a solution of the nonlinear third-order differential equation over 0 < eta < infinity is established in this paper, answering the open question of Vajravelu and Cannon (Appl. Math. Comput. 2006; 181:609-618). That is, we prove with estimates independent of R for solutions of the third-order differential equation on [0,R]. The existence of a solution on 0 < eta < infinity follows from the Ascoli-Arzela Theorem. Furthermore, numerical solutions are obtained and presented through graphs, and the influence of the physical parameter on the flow characteristics is discussed. Copyright (C) 2009 John Wiley & Sons, Ltd.

Keywords

existence results, nonlinear boundary value problems, Runge-Kutta method, Schauder theory, similarity solutions

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