H. KOÇAK ET AL.

199

Heat and Mass Transfer, Vol. 33, No. 3, 2006, pp. 391-

400. doi:10.1016/j.icheatmasstransfer.2005.11.001

[2] D. D. Ganji and A. Sadighi, “Application of He’s Homo-

topy-Perturbation Method to Nonlinear Coupled Systems

of Reaction-Diffusion Equations,” International Journal

of Nonlinear Sciences and Numerical Simulation, Vol. 7,

No. 4, 2006, pp. 411-418.

doi:10.1515/IJNSNS.2006.7.4.411

[3] A. Rajabi, D. D. Ganji and H. Taherian, “Application of

Homotopy Perturbation Method in Nonlinear Heat Con-

duction and Co

Vol. 360, No.

nvection Equations,” Physics Letters A,

4-5, 2007, pp. 570-573.

doi:10.1016/j.physleta.2006.08.079

[4] L. Cveticanin, “Homotopy-Perturbation Method for Pure

Nonlinear Differential Equation,” Chaos, Solitons &

Fractals, Vol. 30, No. 5, 2006, pp. 1221-1230.

doi:10.1016/j.chaos.2005.08.180

[5] J. H. He, “Homotopy Perturbation Method for Bifurca-

tion of Nonlinear Problems,” International Journal of

Nonlinear Sciences and Numerical Simulation, Vol. 6,

No. 2, 2005, pp. 207-208.

[6] J. H. He, “Homotopy Perturbation Method For Solving

Boundary Value Problems,” Physic

No. 1-2, 2006, pp. 87-88.

s Letters A, Vol. 350,

[7] J. H. He, “Limit Cycle and Bifurcation of Nonlinear

Problems,” Chaos, Solitons & Fractals, Vol. 26, No. 3,

2005, pp. 827-833. doi:10.1016/j.chaos.2005.03.007

[8] F. M. Atay, “Van der Pol’s Oscillator under Delayed

Feedback,” Journal of Sound and Vibration, Vol. 218, No.

2, 1998, pp. 333-339. doi:10.1006/jsvi.1998.1843

[9] W. Jiang and J. Wei, “Bifurcation Analysis in Van der

Pol’s Oscillator with Delayed Feedback,” Journal of

Computational and Applied Mathematics, Vol. 213, No. 2

2008, pp. 604-615.

,

doi:10.1016/j.cam.2007.01.041

[10] A. Kimiaeifar, A. R. Saidi, A. R. Sohouli and D. D. Ganji,

“Analysis of Modiﬁed Vander Pol’s Oscillator Using

He’s Parameter-Expanding Methods,” Current Applied

Physics, Vol. 10, No. 1, 2010, pp. 279-283.

doi:10.1016/j.cap.2009.06.006

[11] J. Ghanouchi, H. Labiadh and K. Boubaker, “An Attempt

to Solve the Heat Transfert Equation in a Model of Pyro-

lysis Spray Using 4q-Order m-Boubaker Polynomials,”

International Journal of Heat & Technology, Vol. 26, No.

1, 2008, pp. 49-53.

[12] O. B. Awojoyogbe and K. Boubaker, “A Solution to

Bloch NMR Flow Equations for the Analysis of Homo-

dynamic Functions of Blood Flow System Using m-Bou-

baker Polynomials,” Current Applied Physics, Vol. 9, No.

3, 2009, pp. 278-288. doi:10.1016/j.cap.2008.01.019

[13] H. Labiadh and K. Boubaker, “A Sturm-Liouville Shaped

ials Solution to Heat Equation for

ated

mials B_4q(X) (Named

e and F. Moses,

Characteristic Differential Equation As a Guide to Estab-

lish a Quasi-Polynomial Expression to the Boubaker Po-

lynomials,” Differential Equations and Control Processes,

Vol. 2, No. 2, 2007, pp. 117-133.

[14] S. Slama, J. Bessrour, M. Bouhafs and K. B. Ben Mah-

moud, “Numerical Heat Transfer, Part A: Application,”

An International Journal of Computation and Methodol-

ogy, Vol. 48, No. 6, 2005, pp. 401-404.

[15] S. Slama, M. Bouhafs and K. B. Ben Mahmoud, “A

Boubaker Polynom

Monitoring A3 Point Evolution During Resistance Spot

Welding,” International Journal of Heat and Technology,

Vol. 26, No. 2, 2008, pp. 141-146.

[16] H. Rahmanov, “Triangle Read by Rows: Row n Gives

Coefficients of Boubaker Polynomial B_n(x), Calcul

for X = 2cos(t), Centered by Adding –2cos(nt), Then Di-

vided by 4, in Order of Decreasing Exponents,” OEIS

(Encyclopedia of Integer Sequences), A160242.

[17] H. Rahmanov, “Triangle Read by Rows: Row n Gives

Values of the 4q-28Boubaker Polyno

after Boubaker Boubaker (1897-1966)), Calculated for X

= 1 (or –1),” OEIS (Encyclopedia of Integer Sequences),

A162180.

[18] S. Tabatabaei, T. Zhao, O. Awojoyogb

“Cut-Off Cooling Velocity Profiling Inside a Keyhole

Model Using the Boubaker Polynomials Expansion

Scheme,” Heat and Mass Transfer, Vol. 45, No. 10, 2009,

pp. 1247-1255. doi:10.1007/s00231-009-0493-x

[19] S. Fridjine and M. Amlouk, “A New Parameter: An

ABACUS for Optimizig Functional Materials Using the

Boubaker Polynomials Expansion Scheme,” Modern

Physics Letters B, Vol. 23, No. 17, 2009, pp. 2179-2182.

doi:10.1142/S0217984909020321

[20] A. Belhadj, J. Bessrour, M. Bouhafs and L. Barrallier,

“Experimental and Theoretical Cooling Velocity Profile

Inside Laser Welded Metals Using Keyhole Approxima-

tion and Boubaker Polynomials Expansion,” Journal of

Thermal Analysis and Calorimetry, Vol. 97, No. 3, 2009,

pp. 911-920. doi:10.1007/s10973-009-0094-4

[21] A. Belhadj, O. Onyango and N. Rozibaeva, “Boubaker

Polynomials Expansion Scheme-Related Heat Transfer

Investigation Inside Keyhole Model,” Journal of Ther-

mophysics Heat Transfer, Vol. 23, No. 6, 2009, pp. 639-

642.

[22] A. Chaouachi, K. Boubaker, M. Amlouk and H. Bou-

zouita, “Enhancement of Pyrolysis Spray Disposal Per-

formance Using Thermal Time-Response to Precursor

Uniform Deposition,” The European Physical Journal -

Applied Physics, Vol. 37, No. 1, 2007, pp. 105-109.

doi:10.1051/epjap:2007005

[23] D. H. Zhang and F. W. Li, “A Boubaker Polynomials

Expansion Scheme BPES-Related Analytical Solution to

Williams-Brinkmann Stagnation Point Flow Equation at a

Blunt Body,” Journal of Engineering Physics and Ther-

mophysics, Vol. 84, No. 3, 2009, pp. 618-623.

[24] Z. L. Tao, “Frequency–Amplitude Relationship of Non-

linear Oscillators by He’s Parameter-Expanding Me-

thod,” Chaos, Solitons & Fractals, Vol. 41, No. 2, 2009,

pp. 642-645. doi:10.1016/j.chaos.2008.02.036

[25] L. Xu, “He’s Parameter-Expanding Methods for Strongly

Nonlinear Oscillators,” Journal of Computational and

Applied Mathematics, Vol. 207, No. 1, 2007, pp. 148-154.

doi:10.1016/j.cam.2006.07.020

[26] D. D. Ganji, M. Rafei, A. Sadighi and Z. Z. Ganji, “A

Comparative Comparison of He’s Method with Perturba-

Copyright © 2011 SciRes. CS