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Numerical solution of Duffing equation by the Laplace decomposition algorithm. (English) Zbl 1096.65067

Summary: The Laplace decomposition algorithm (LDA) is a numerical algorithm and can be adapted to solve Duffing equations. This paper both describes the principle of LDA and discusses its advantages and drawbacks. Concrete example are also studied to show with numerical results how the LDA works efficiently.

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
44A10 Laplace transform
34A34 Nonlinear ordinary differential equations and systems
65R10 Numerical methods for integral transforms

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References:

[1] Adomian, G., A review of the decomposition method and some recent results for nonlinear equations, Comput. math. appl., 21, 5, 101-127, (1991) · Zbl 0732.35003
[2] Adomian, G., Solving frontier problems of physics: the decomposition method, (1994), Kluwer Dordrecht · Zbl 0802.65122
[3] Adomian, G., Solution of the Thomas-Fermi equation, Appl. math. lett., 11, 3, 131-133, (1998) · Zbl 0947.34501
[4] Biazar, J.; Babolian, E.; Kember, G.; Nouri, A.; Islam, R., An alternate algorithm for computing Adomian polynomials in special cases, Appl. math. comput., 138, 523-529, (2003) · Zbl 1027.65076
[5] Boyd, J., Pade approximant algorithm for solving nonlinear ordinary differential equation boundary value problems on an unbounded domain, Comput. phys., 11, 3, 299-303, (1997)
[6] Buchanan, J.L.; Turner, P.R., Numerical methods and analysis, (1992), McGraw-Hill Singapore
[7] He, Ji-Huan, Variational approach to the Thomas-Fermi equation, Appl. math. comput., 143, 533-535, (2003) · Zbl 1022.65083
[8] He, J.-H., Variational approach to the sixth-order boundary value problems, Appl. math. comput., 143, 537-538, (2003) · Zbl 1025.65043
[9] He, J.-H., Variational approach to the Lane-Emden equation, Appl. math. comput., 143, 539-541, (2003) · Zbl 1022.65076
[10] Hon, Y.C., A decomposition method for the Thomas-Fermi equation, SEA bull. math., 20, 3, 55-58, (1996) · Zbl 0858.34017
[11] Jiao, J.C.; Yamamoto, Y.; Dang, C.; Hao, Y., An after treatment technique for improving the accuracy of adomian’s decomposition method, Comput. math. appl., 43, 783-798, (2002) · Zbl 1005.34006
[12] Khuri, S.A., A Laplace decomposition algorithm applied to a class of nonlinear differential equations, J. appl. math., 1, 4, 141-155, (2001) · Zbl 0996.65068
[13] Khuri, S.A., An alternative solution algorithm for the nonlinear generalized Emden-Fowler equation, Int. J. nonlin. sci. numer. simul., 2, 3, 299-302, (2001) · Zbl 1072.34503
[14] Lim, C.W.; Wu, B.S., A new analytical approach to the Duffing-harmonic oscillator, Phys. lett. A, 311, 365-373, (2003) · Zbl 1055.70009
[15] Murakami, W.; Murakami, C.; Hirose, K.; Ichikawa, Y.H., Integrable duffing’s maps and solutions of the Duffing equation, Chaos solitions fractals, 15, 425-443, (2003) · Zbl 1031.37047
[16] Potts, R.B., Exact solution of a difference approximation to duffing’s equation, J. aust. math. soc. (ser. B), 23, 349-356, (1981) · Zbl 0479.65045
[17] Potts, R.B., Best difference equation approximation to duffing’s equation, J. aust. math. soc. (ser. B), 23, 64-77, (1982) · Zbl 0475.34008
[18] Wazwaz, A.M., A reliable modification of adomian’s decomposition method, Appl. math. comput., 102, 77-86, (1999) · Zbl 0928.65083
[19] Wazwaz, A.M., The modified decomposition method and pade approximant for solving the Thomas-Fermi equation, Appl. math. comput., 105, 11-19, (1999) · Zbl 0956.65064
[20] Wazwaz, A.M., A new algorithm for calculating Adomian polynomials for nonlinear operators, Appl. math. comput., 111, 53-69, (2000) · Zbl 1023.65108
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