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Solutions of a class of singular second-order IVPs by homotopy-perturbation method. (English) Zbl 1203.65124
Summary: Solutions of a class of singular initial value problems (IVPs) in the second-order ordinary differential equations (ODEs) by homotopy-perturbation method (HPM) are presented. HPM yields solutions in convergent series forms with easily computable terms, and in some cases, yields exact solutions in one iteration. Comparisons with the exact solutions and the solutions obtained by the decomposition method show the potential of HPM in solving singular problems.

MSC:
65L99 Numerical methods for ordinary differential equations
34A45 Theoretical approximation of solutions to ordinary differential equations
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
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[1] Chandrasekhar, S., Introduction to the study of stellar structure, (1967), Dover New York · Zbl 0079.23901
[2] Davis, H.T., Introduction to nonlinear differential and integral equations, (1962), Dover New York
[3] Richardson, O.U., The emission of electricity from hot bodies, (1921), Zongmans Green and Company London
[4] Shawagfeh, N.T., J. math. phys., 34, 4364, (1993)
[5] Wazwaz, A.M., Appl. math. comput., 118, 287, (2001)
[6] Wazwaz, A.M., Appl. math. comput., 128, 45, (2002)
[7] Wazwaz, A.M., Appl. math. comput., 173, 165, (2006)
[8] Adomian, G., Comput. math. appl., 27, 145, (1994)
[9] He, J.H., Comput. methods appl. mech. engrg., 178, 257, (1999)
[10] He, J.H., Int. J. non-linear mech., 35, 37, (2000)
[11] He, J.H., Appl. math. comput., 135, 73, (2003)
[12] He, J.H., Int. J. nonlinear sci. numer. simul., 6, 207, (2005)
[13] He, J.H., Chaos solitons fractals, 26, 695, (2005)
[14] He, J.H., Non-perturbative methods for strongly nonlinear problems, (2006), Die Deutsche Bibliothek Germany
[15] He, J.H., Int. J. mod. phys. B, 20, 1141, (2006)
[16] He, J.H., Phys. lett. A, 350, 87, (2006)
[17] Mo, J.Q.; Lin, W.T., Chin. phys., 14, 875, (2005)
[18] El-Shahed, L.M., Int. J. nonlinear sci. numer. simul., 6, 163, (2005)
[19] Cveticanin, L., J. sound vibration, 285, 1171, (2005)
[20] Ganji, D.D.; Rajabi, A., Int. comm. heat mass transfer, 33, 391, (2006)
[21] Ganji, D.D.; Sadighi, A., Int. J. nonlinear sci. numer. simul., 7, 4, 411, (2006)
[22] Siddiqui, A.M.; Mahmood, R.; Ghori, Q.K., Int. J. nonlinear sci. numer. simul., 7, 7, (2006)
[23] Cai, X.C.; Wu, W.Y.; Li, M.S., Int. J. nonlinear sci. numer. simul., 7, 109, (2006)
[24] Rajabi, A.; Ganji, D.D.; Taherian, H., Phys. lett. A, 360, 570, (2007)
[25] Noor, M.A.; Mohyud-Din, S.T., Math. comput. modelling, 45, 7-8, 954, (2007)
[26] D.D. Ganji, A. Sadighi, J. Comput. Appl. Math., doi:10.1016/j.cam.2006.07.030, in press
[27] Rajabi, A., Phys. lett. A, 364, 33, (2007)
[28] Arief, P.D.; Hayat, T.; Asghar, S., Int. J. nonlinear sci. numer. simul., 7, 4, 399, (2006)
[29] He, J.H., Int. J. mod. phys. B, 20, 18, 2561, (2006)
[30] Zhang, L.N.; He, J.H., Math. prob. engrg., Art. No. 83878, 1, (2006)
[31] Ramos, J.I., Appl. math. comput., 161, 525, (2005)
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