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Journal of Applied Mathematics
Volume 2015 (2015), Article ID 864190, 5 pages
http://dx.doi.org/10.1155/2015/864190
Research Article

On the Study of Oscillating Viscous Flows by Using the Adomian-Padé Approximation

1Division of Mathematics, General Education Center, Chienkuo Technology University, Changhua City 500, Taiwan
2International Wave Dynamics Research Center, National Cheng Kung University, Tainan 701, Taiwan

Received 8 November 2014; Accepted 2 April 2015

Academic Editor: Charalampos Tsitouras

Copyright © 2015 Chi-Min Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The Adomian-Padé technique is applied to examine two oscillating viscous flows, the Stokes’ second problem and the pressure-driven pulsating flow. Main purposes for studying oscillating flows are not only to verify the accuracy of the approximation solution, but also to provide a basis for analyzing more problems by the present method with the help of Fourier analysis. Results show that the Adomian-Padé approximation presents a very excellent behavior in comparison with the exact solution of Stokes’ second problem. For the pulsating flow, only the Adomian decomposition method is required to perform the calculation as the fluid domain is finite where the Padé approximant may not provide a better solution. Based on present results, more problems can be mathematically solved by using the Adomian-Padé technique, the Fourier analysis, and powerful computers.