Semi Numerical Solution for a Boundary Value Problem


The flow of viscous incompressible fluid through a tube is considered. The similarity transformation is used to reduce the governing equations into nonlinear ordinary differential equation. The solution procedure includes application of long series analysis with polynomial coefficients. The series representing physical parameters ( ) reveal qualitative features which are comparable to pure numerical results. The analysis enables in extending region of validity. A complete description of the solutions is presented.

Share and Cite:

N. Pai, N. Katagi and K. Chavaraddi, "Semi Numerical Solution for a Boundary Value Problem," American Journal of Computational Mathematics, Vol. 3 No. 1, 2013, pp. 43-47. doi: 10.4236/ajcm.2013.31006.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] M. Y. Jaffrin and A. H. Shapiro, “Peristatic Pumping,” Annual Review of Fluid Mechanics, Vol. 3, 1971, pp. 13-36. doi:10.1146/annurev.fl.03.010171.000305
[2] C. D. Bertram, C. J. Reymond and T. J. Pedley, “Mapping of Instabilities during Flow through Collapsed Tubes of Differing Length,” Journal of Fluids and Structures, Vol. 4, No. 2, 1990, pp. 125-154. doi:10.1016/0889-9746(90)90058-D
[3] T. W. Secomb, “Flow in a Channel with Pulsating Wall,” Journal of Fluid Mechanics, Vol. 88, No. 2, 1978, pp. 273-287. doi:10.1017/S0022112078002104
[4] M. Van Dyke, “Mathematical Approach in Hydrodynamics,” SIAM, Philadelphia, 1997.
[5] N. M. Bujurke and N. P. Pai, “Computer Extended Series Solution for Flow between Squeezing Plates,” Fluid Dynamics Research, Vol. 16, No. 2-3, 1995, pp. 167-183. doi:10.1016/0169-5983(94)00058-8
[6] F. M. Skalak and C. Y. Wang, “On the Unsteady Squeezing of a Viscous Fluid from a Tube,” Journal of the Australian Mathematical Society, Vol. 21, 1979, pp. 65-74.
[7] M. Van Dyke, “Analysis and Improvement of Perturbation Series,” Mathematics & Physical Sciences, Vol. 27, No. 4, 1974, pp. 423-456. doi:10.1093/qjmam/27.4.423
[8] C. M. Bender and S. A. Orszag, “Advanced Mathematical Methods for Scientists and Engineers,” 3rd International Edition, Springer, New York, 1987.

Copyright © 2022 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.