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Modified Adomian decomposition method for specific second order ordinary differential equations. (English) Zbl 1114.65078
Summary: An efficient modification of Adomian decomposition method is introduced for solving second order ordinary differential equations. The proposed method can be applied to singular and nonsingular problems. The scheme is tested for some examples and the obtained results demonstrate efficiency of the proposed method.

65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
Full Text: DOI
[1] Adomian, G., A review of the decomposition method and some recent results for nonlinear equation, Math. comput. model., 13, 7, 17, (1992) · Zbl 0713.65051
[2] Adomian, G., Solving frontier problems of physics: the decomposition method, (1994), Kluwer Boston, MA · Zbl 0802.65122
[3] Adomian, G.; Rach, R., Noise terms in decomposition series solution, Comput. math. appl., 24, 11, 61, (1992) · Zbl 0777.35018
[4] Adomian, G.; Rach, R.; Shawagfeh, N.T., On the analysis solution of lane – emden equation, Found. phys. lett., 8, 2, 161, (1995)
[5] Adomian, G., Differential coefficients with singular coefficients, Appl. math. comput., 47, 179, (1992) · Zbl 0748.65066
[6] Hosseini, M.M., Adomian decomposition method with Chebyshev polynomials, Appl. math. comput., 175, 1685-1693, (2006) · Zbl 1093.65073
[7] Wazwaz, A.M., A first course in integral equations, (1997), World Scientific Singapore
[8] Wazwaz, A.M., A reliable modification of Adomian decomposition method, Appl. math. comput., 102, 77, (1999) · Zbl 0928.65083
[9] Wazwaz, A.M., Analytical approximations and pade’ approximations for volterra’s population model, Appl. math. comput., 100, 13, (1999) · Zbl 0953.92026
[10] Wazwaz, A.M., A new algorithm for calculating Adomian polynomials for nonlinear operators, Appl. math. comput., 111, 1, 33, (2000)
[11] Wazwaz, A.M., A new method for solving singular initial value problems in the second-order ordinary differential equations, Appl. math. comput., 128, 45-57, (2002) · Zbl 1030.34004
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