A New Analytical of the Homotopy Analysis Method for Solving Singular Two-Point BVPs
DOI:
https://doi.org/10.24203/x4y46q42Keywords:
homotopy analysis method; Singular two-point boundary value problems.Abstract
In this paper, we will introduce a new adjustment of the homotopy analysis method (HAM) to obtain approximate or accurate solutions to problems BVPs. The results showed that this proposed amendment is very effective compared to the basic homotopy analysis method (HAM), where in most cases solutions are accurate in the first iteration. Some examples will be given to illustrate the suggested method.
References
A.M. Siddiqui, M. Ahmed, Q.K. Ghori, Int. J. Nonlinear Sci. Numer. Simul. 7 (2005) 15.
A. S.Bataineh, M.S. Nooran, I.Hashim, On a new reliable modification of homotopy analysis method, Communications in nonlinear and numerical simulation, volume 14, issue 2, 2009, 409-423.
A.S. Bataineh, M.S. Noorani and I. Hashim, 2008. Phys. Lett., A 372:4062.
A.S. Bataineh, Avoid the uncontrollability problems of the nonzero endpoint conditions via homotopy analysis method, Appl. Comput. Math., V.13, N.1,2014, pp. 1-13.
A.S.V. Ravi Kanth, Y.N. Reddy, Appl. Math. Comput. 170 (2005) 733.
H.N. Hassan and M.A. El-Tawil , "A new technique of using homotopy analysis method for solving high-order nonlinear differential equations, Mathematical Method in the Applied Sciences , vol.34,no.6,pp.728-742,2011.
I.T. Abu-Zaid, M.A. El-Gebeily, Arab. J. Math. Sci. 1 (1995) 25.
K. Al-Khaled, Chaos Solitons Fractals 33 (2007) 678.
L.u. Junfeng, J. Comput. Appl. Math. 207 (2007) 92.
M. Cui, F. Geng, J. Comput. Appl. Math. 205 (2007) 6.
M.A. El-Tawil, and S.N. Huseen , The q-Homotopy Analysis Method (q-HAM), International Journal of Applied mathematics and mechanics, 8 (15):51-75, 2012.
M.A. El-Tawil, and S.N. Huseen,On Convergence of The q-Homotopy Analysis Method, Int. J. Contemp. Math. Sciences, Vol. 8, 2013, no. 10, 481 –497.
S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Dover, New York, 1981.
S.J. Liao, The Proposed Homotopy Analysis Techniques for the Solution of Nonlinear Problems, Ph.D. Dissertation, Shanghai Jiao Tong University, Shanghai; 1992 (in English).
S.N. Huseen and H.A. Mkharrib , On a New Modification of Homotopy Analysis Method for Solving Nonlinear Nonhomogeneous Differential Equations, Asian Journal of Fuzzy and Applied Mathematics . Volume 06 – Issue 02, October 2018
Z. Ayati ,J. Biazar ,B. Gharedaghi ,The application of modified homotopy analysis method for solving linear and non-linear inhomogeneous Klein-Gordon equations, Acta Universitatis Apulensis, no. 39,pp. 31-40 ,2014.
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