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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.

The Adomian decomposition method has been widely studied and applied to solve mathematical problems [

As all decomposed terms except the first one are calculated by integration, the solution is usually expressed in a form of a polynomial of the variable of integration (the temporal or spatial variable). Therefore, the applicable range of the Adomian decomposed solution will diverge quickly while this integration variable grows. To overcome the weakness, the Padé approximation is adopted to improve the accuracy of the solution. The main idea of Padé approximant is to transfer the original polynomial into a rational function of the order

In this paper two cases of oscillating viscous flows will be investigated by using the Adomian-Padé approximation. The main reason why we study oscillating flows is that the present study can provide a basis for analyzing more problems while applying the Fourier analysis. The organization of this paper is as follows. In Section

A viscous flow generated by an oscillating plate below is the well-known Stokes’ second problem. The plate is located at the plane

Now the Adomian-Padé method is applied to solve the problem. First we define the operator

Comparison of Padé

Comparison of Padé

The present method can play an important role in practical cases. For example, if the boundary conditions at the plate can be measured by current meters or other facilities, velocity profile at any elevation

Another oscillating flow, the pressure-driven pulsating flow, is studied in this section. This flow describes that a fluid bounded by two parallel plates located at

Ratios of polynomial solution and its Padé

This paper presents the examination of Stokes’ second problem and the pressure-driven pulsating flow by applying the Adomian-Padé technique. For Stokes’ second problem, higher-order Adomian-Padé solution behaves very well in comparison with the exact solution while the spatial parameter grows. For pressure-driven pulsating flow, the Adomian approximation provides satisfactory results and the application of the Padé approximant may be unnecessary for the case of the finite domain. The above results demonstrate that the method used in this paper can be applied to solve more complicated problems with the help of the Fourier analysis and powerful computers.

The author declares that there is no conflict of interests regarding the publication of this paper.

Financial support from the Ministry of Science and Technology of Taiwan through Grants NSC 101-2221-E-270-001-MY2 and MOST 104-2911-I-006-301 is acknowledged.