Homotopy Analysis Decomposition Method for the Solution of Viscous Boundary Layer Flow Due to a Moving Sheet

Abstract

This paper investigates a new approach called Homotopy Analysis Decomposition Method (HADM) for solving nonlinear differential equations, the method was developed by incorporating Adomian polynomial into Homotopy Analysis Method. The Adomian polynomial was used to decompose the nonlinear term in the equation then apply the scheme of homotopy analysis method. The accuracy and efficiency of the proposed method was validated by considering algebraically decaying viscous boundary layer  flow due to a moving sheet. Diagonal Pade approximation was used to get the skin friction. The obtained results were presented along with other methods in the literature in tabular form to show the computational efficiency of the new approach. The results were found to agree with those in literature. Owing to its small size of computation, the method is not aected by discretization error as the results are presented in form of polynomials.

Keywords:
Homotopy Analysis Decomposition Method, Homotopy Analysis Method, Nonlinear term, Adomian Polynomial, Skin friction.

Article Details

How to Cite
Alao, S., Oderinu, R., Akinpelu, F., & Akinola, E. (2019). Homotopy Analysis Decomposition Method for the Solution of Viscous Boundary Layer Flow Due to a Moving Sheet. Journal of Advances in Mathematics and Computer Science, 32(5), 1-7. https://doi.org/10.9734/jamcs/2019/v32i530157
Section
Original Research Article

References

Khan Y, Faraz N. Application of modified laplace decomposition for solving boundary layer equation. Journal of King Saud University (Science). 2011;23:115-119.
DOI:10.1016/j.jksus.2010.06.018

Sakiadis BC. Boundary-layer behavior on continuous solid surface II: Boundary layer on a continuous at surface. AIChE. J. 1961;7:221-225.

Adomian G. Solving frontier problems of physics: The decomposition method. Kluwer Academic Publishers, Boston; 1994.

Ahmed AH, Kirtiwant PG. Modified adomian decomposition method for solving fuzzy volterra- fredholm integral equation. The Journal of Indian Mathematical Society. 2018;85:53-69.
DOI:10.18311/jims/2018/16260

Liao SJ. On the homotopy analysis method for nonlinear problems. Applied Mathematics and Computation. 2004;147:499513.
DOI:10.1016/S0096-3003(02)00790-7

Hussain SA, Muhammad S, Ali G, Shah SIA, Ishaq M, Shah Z, Khan H, Tahir M, Naeem M. A bioconvection model for squeezing ow between parallel plates containing gyrotactic microorganisms with impact of thermal radiation and heat generation/absorption. Journal of Advances in Mathematics and Computer Science. 2018;27:1-22.
DOI: 10.9734/JAMCS/2018/41767

Muhammad S, Shah SIA, Ali G, Ishaq M, Hussain SA, Ullah H. Squeezing nano fluid flow between two parallel plates under the in uence of MHD and thermal radiation. Asian Research Journal of Mathematics. 2018;10:1-20.
DOI: 10.9734/ARJOM/2018/42092

Momani SM, Abuasad S, Odibat Z. Variational iteration method for solving nonlinear boundary value problems. Applied Mathematics and Computation. 2006;183:1351-1358.
DOI: 10.1016/j.amc.2006.05.138

Guo-Cheng W, Dumitru B. Variational iteration method for the burgers ow with fractional
derivatives-new lagrange multipliers. Applied Mathematical Modelling. 2013;37:6183-6190.

Ganji DD, Sadighi A. Application of hes homotopy perturbation method to nonlinear coupled systems of reaction diffusion equations. Int. J. Nonl. Sci. and Num. Simu. 2006;7:411-418.
Doi:10.1515/IJNSNS.2006.7.4.411

Mojtaba B. Analytic approximate solution for a flow of a second-grade viscoelastic fluid in a converging channel. Journal of Applied Mechanics and Technical Physics. 2018;59:72-78.
DOI:10.1134/S0021894418010091

Alao S, Salaudeen KA, Akinola EI, Akinboro FS, Akinpelu FO. Weighted residual method for the squeezing
ow between parallel walls or plates. American International Journal of Research in Science, Engineering, Technology and Mathematics. 2017;17:42-46. AIJRSTEM 17-309.

Oderinu RA, Aregbesola YAS. Analysis of skin friction in MHD falkner-skan ow problem. Journal of the Nigerian Mathematical Society. 2015;34:195-199.

Baker GA. Essentials of pade approximants. London: Academic Press; 1975.

Boyd JP. Pade approximant algorithm for solving nonlinear ordinary differential equation boundary value problems on an unbounded domain. Computers in Physics. 1997;11:299-303.
DOI.org/10.1063/1.168606

Wazwaz AM. A study on a boundary-layer equation arising in an incompressible fluid. Applied Mathematics and Computation. 1997;87:199-204.
DOI.org/10.1016/S0096-3003(96)00281-0

Noor MA, Mohyud-Din ST. Variational iteration method for unsteady
ow of gas through a
porous medium using he's polynomials and pade approximants. Computers and Mathematics with Applications. 2009;58:2182-2189.
DOI:10.1016/j.camwa.2009.03.016

Noor MA, Mohyud-Din ST. Modified variational iteration method for a boundary layer problem in unbounded domain. International Journal of Nonlinear Science. 2009;7:426-430. IJNS.2009.06.30/243.

Khan Y, Smarda Z. A novel computing approach for third order boundary layer equation. Sains Malaysiana. 2012;1489-1493.

Xu L. He's homotopy perturbation method for a boundary layer equation in unbounded domain. Computers and Mathematics with Applications. 2007;54:1067-1070.
DOI.org/10.1016/j.camwa.2006.12.052