O. TASBOZAN ET AL.

Copyright © 2012 SciRes. OJAppS

197

Shanghai Jiao Tong University, Shanghai, 1992.

[5] S. J. Liao, “Beyond Perturbation: Introduction to the

Homotopy Analysis Method,” Chapman and Hall/CRC

Press, Boca Raton, 2003. doi:10.1201/9780203491164

[6] S. J. Liao, “Homotopy Analysis Method: A New Ana-

lytical Technique for Nonlinear Problems,” Communica-

tions in Nonlinear Science and Numerical. Simulations,

Vol. 2, No. 2, 1997, pp. 95-100.

doi:10.1016/S1007-5704(97)90047-2

[7] S. J. Liao, “On the Homotopy Analysis Method for

Nonlinear Problems,” Applied Mathematics and Compu-

tation, Vol. 147, No. 2, 2004, pp. 499-513.

doi:10.1016/S0096-3003(02)00790-7

[8] S. J. Liao, “Notes on the Homotopy Analysis Method:

Some Definitions and Theorems,” Communications in

Nonlinear Science and Numerical Simulations, Vol. 14,

No. 4, 2009, pp. 983-997.

doi:10.1016/j.cnsns.2008.04.013

[9] S. Abbasbandy, “The Application of Homotopy Analysis

Method to Solve a Generalized Hirota-Satsuma Coupled

KdV Equation,” Physics Letters A, Vol. 361, No. 6, 2007,

pp. 478-483. doi:10.1016/ j.physleta.2006.09.105

[10] E. Babolian and J. Saeidian, “Analytic Approximate So-

lutions to Burgers, Fisher, Huxley Equations and Two

Combined Forms of These Equations,” Communications

in Nonlinear Science and Numerical Simulation, Vol. 14,

No. 5, 2009, pp. 1984-1992.

doi:10.1116/j.cnsns.2008.07.019

[11] A. Fakhari, G. Domairry and Ebrahimpour, “Approximate

Explicit Solutions of Nonlinear BBMB Equations by

Homotopy Analysis Method and Comparison with the

Exact Solution,” Physics Letters A, Vol. 368, No. 1-2,

2007, pp. 64-68. doi:10.1116/j.physleta.2007.03.062

[12] M. M. Rashidi, G. Domairry, A. Doosthosseini and S.

Dinarvand, “Explicit Approximate Solution of the Cou-

pled KdV Equations by Using the Homotopy Analysis

Method,” International Journal of Mathematical Analysis,

Vol. 2, No. 12, 2008, pp. 581-589.

[13] Mustafa Inc., “On Numerical Solution of Burgers’ Equa-

tion by Homotopy Analysis Method,” Physics Letters A,

Vol. 372, No. 4, 2008, pp. 356-360.

doi:10.1016/j.physleta.2007.07.057

[14] A. S. Bataineh, M. S. M. Noorani and I. Hashim, “Ap-

proximate Analytical Solutions of Systems of PDEs by

Homotopy Analysis Method,” Computers and Mathe-

matics with Applications, Vol. 55, No. 12, 2008, pp.

2913-2923. doi:10.1016/j.camwa.2007.11.022

[15] S. Abbasbandy, “The Application of Homotopy Analysis

Method to Nonlinear Equations Arising in Heat Trans-

fer,” Physics Letters A, Vol. 360, No. 1, 2006, pp. 109-

113. doi:10.1016/j.physleta.2006.07.065

[16] T. Hayat and M. Sajid, “On Analytic Solution for Thin

Film Flow of a Forth Grade Fluid Down a Vertical Cyl-

inder,” Physics Letters A, Vol. 361, No. 4-5, 2007, pp.

316-322. doi:10.1016/j.physleta.2006.09.060

[17] H. Xu and J. Cang, “Analysis of a Time Fractional

Wave-Like Equation with the Homotopy Analysis Method,”

Physics Letters A, Vol. 372, No. 8, 2008, pp. 1250-1255.

doi:10.1016/j.physleta.2007.09.039

[18] L. Song and H. Q. Zhang, “Application of Homotopy

Analysis Method to Fractional KdV-Burgers-Kuramoto

Equation,” Physics Letters A, Vol. 367, No. 1-2, 2007, pp.

88-94. doi:10.1016/j.physleta.2007.02.083

[19] D. B. Cao, J. R. Yanb and Y. Zhang, “Exact Solutions for

a New Coupled MKdV Equations and a Coupled KdV

Equations,” Physics Letters A, Vol. 279, No. 1-2, 2002,

pp. 68-74. doi:10.1016/S0375-9601(02)00376-6