Numerical solution of Duffing equation by the Laplace decomposition algorithm

Adomian, 1991, A review of the decomposition method and some recent results for nonlinear equations, Comput. Math. Appl., 21, 101, 10.1016/0898-1221(91)90220-X Adomian, 1994 Adomian, 1998, Solution of the Thomas–Fermi equation, Appl. Math. Lett., 11, 131, 10.1016/S0893-9659(98)00046-9 Biazar, 2003, An alternate algorithm for computing Adomian polynomials in special cases, Appl. Math. Comput., 138, 523, 10.1016/S0096-3003(02)00174-1 Boyd, 1997, Pade approximant algorithm for solving nonlinear ordinary differential equation boundary value problems on an unbounded domain, Comput. Phys., 11, 299, 10.1063/1.168606 Buchanan, 1992 He, 2003, Variational approach to the Thomas–Fermi equation, Appl. Math. Comput., 143, 533, 10.1016/S0096-3003(02)00380-6 He, 2003, Variational approach to the sixth-order boundary value problems, Appl. Math. Comput., 143, 537, 10.1016/S0096-3003(02)00381-8 He, 2003, Variational approach to the Lane–Emden equation, Appl. Math. Comput., 143, 539, 10.1016/S0096-3003(02)00382-X Hon, 1996, A decomposition method for the Thomas–Fermi equation, SEA Bull. Math., 20, 55 Jiao, 2002, An after treatment technique for improving the accuracy of Adomian’s decomposition method, Comput. Math. Appl., 43, 783, 10.1016/S0898-1221(01)00321-2 Khuri, 2001, A Laplace decomposition algorithm applied to a class of nonlinear differential equations, J. Appl. Math., 1, 141, 10.1155/S1110757X01000183 Khuri, 2001, An alternative solution algorithm for the nonlinear generalized Emden–Fowler equation, Int. J. Nonlin. Sci. Numer. Simul., 2, 299, 10.1515/IJNSNS.2001.2.3.299 Lim, 2003, A new analytical approach to the Duffing-harmonic oscillator, Phys. Lett. A, 311, 365, 10.1016/S0375-9601(03)00513-9 Murakami, 2003, Integrable Duffing’s maps and solutions of the Duffing equation, Chaos Solitions Fractals, 15, 425, 10.1016/S0960-0779(02)00089-9 Potts, 1981, Exact solution of a difference approximation to Duffing’s equation, J. Aust. Math. Soc. (Ser. B), 23, 349, 10.1017/S0334270000000308 Potts, 1982, Best difference equation approximation to Duffing’s equation, J. Aust. Math. Soc. (Ser. B), 23, 64, 10.1017/S0334270000000060 Wazwaz, 1999, A reliable modification of Adomian’s decomposition method, Appl. Math. Comput., 102, 77, 10.1016/S0096-3003(98)10024-3 Wazwaz, 1999, The modified decomposition method and Pade approximant for solving the Thomas–Fermi equation, Appl. Math. Comput., 105, 11, 10.1016/S0096-3003(98)10090-5 Wazwaz, 2000, A new algorithm for calculating Adomian polynomials for nonlinear operators, Appl. Math. Comput., 111, 53, 10.1016/S0096-3003(99)00063-6