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Approximate solutions of singular two-point BVPs by modified homotopy analysis method. (English) Zbl 1220.34026
Summary: In this Letter, approximate solutions of singular two-point boundary value problems (BVPs) are obtained by the modified homotopy analysis methods (MHAM). MHAM provides a convenient way of controlling the convergence region and rate of the series solution. The numerical tests show the capability of MHAM for singular BVPs.

MSC:
34B09 Boundary eigenvalue problems for ordinary differential equations
34B16 Singular nonlinear boundary value problems for ordinary differential equations
65H20 Global methods, including homotopy approaches to the numerical solution of nonlinear equations
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[1] Chandrasekhar, S., Hydrodynamic and hydromagnetic stability, (1981), Dover New York · Zbl 0142.44103
[2] Al-Khaled, K., Chaos solitons fractals, 33, 678, (2007)
[3] Junfeng, L.u., J. comput. appl. math., 207, 92, (2007)
[4] Abu-Zaid, I.T.; El-Gebeily, M.A., Arab. J. math. sci., 1, 25, (1995)
[5] Ravi Kanth, A.S.V.; Reddy, Y.N., Appl. math. comput., 170, 733, (2005)
[6] Siddiqui, A.M.; Ahmed, M.; Ghori, Q.K., Int. J. nonlinear sci. numer. simul., 7, 15, (2005)
[7] S.J. Liao, The proposed homotopy analysis techniques for the solution of nonlinear problems, PhD Dissertation, Shanghai Jiao Tong University, Shanghai, 1992 (in English)
[8] Liao, S.J., Beyond perturbation: introduction to the homotopy analysis method, (2003), CRC Press/Chapman and Hall Boca Raton
[9] Liao, S.J., Int. J. nonlinear mech., 30, 371, (1995)
[10] Liao, S.J., Int. J. nonlinear mech., 32, 815, (1997)
[11] Liao, S.J., Int. J. nonlinear mech., 34, 759, (1999)
[12] Liao, S.J., Appl. math. comput., 147, 499, (2004)
[13] Liao, S.J.; Pop, I., Int. J. heat mass transfer, 47, 75, (2004)
[14] Liao, S.J., Appl. math. comput., 169, 1186, (2005)
[15] Liao, S.J., Int. J. heat mass transfer, 48, 2529, (2005)
[16] Ayub, M.; Rasheed, A.; Hayat, T., Int. J. eng. sci., 41, 2091, (2003)
[17] Hayat, T.; Khan, M.; Asghar, S., Acta mech., 168, 213, (2004)
[18] Hayat, T.; Khan, M., Nonlinear dyn., 42, 395, (2005)
[19] Tan, Y.; Abbasbandy, S., Commun. nonlinear sci. numer. simul., 13, 539, (2008)
[20] Abbasbandy, S., Phys. lett. A, 360, 109, (2006)
[21] Abbasbandy, S., Phys. lett. A, 361, 478, (2007) · Zbl 1273.65156
[22] Bataineh, A.S.; Noorani, M.S.M.; Hashim, I., in press
[23] Bataineh, A.S.; Noorani, M.S.M.; Hashim, I., Phys. lett. A, 371, 72, (2007)
[24] Bataineh, A.S.; Noorani, M.S.M.; Hashim, I., Phys. lett. A, 372, 613, (2008)
[25] A.S. Bataineh, M.S.M. Noorani, I. Hashim, Comput. Math. Appl., in press
[26] Bataineh, A.S.; Noorani, M.S.M.; Hashim, I., in press
[27] Bataineh, A.S.; Noorani, M.S.M.; Hashim, I., in press
[28] Cui, M.; Geng, F., J. comput. appl. math., 205, 6, (2007)
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