Accuracy of the Adomian decomposition method applied to the Lorenz system

I. Hashim; M. S.M. Noorani; R. Ahmad; S. A. Bakar; E. S. Ismail; A. M. Zakaria

doi:10.1016/j.chaos.2005.08.135

Accuracy of the Adomian decomposition method applied to the Lorenz system

I. Hashim
, M. S.M. Noorani
, R. Ahmad
, S. A. Bakar
, E. S. Ismail
, A. M. Zakaria

Universiti Kebangsaan Malaysia

Research output: Contribution to journal › Article › peer-review

95 Scopus citations

Abstract

In this paper, the Adomian decomposition method (ADM) is applied to the famous Lorenz system. The ADM yields an analytical solution in terms of a rapidly convergent infinite power series with easily computable terms. Comparisons between the decomposition solutions and the fourth-order Runge-Kutta (RK4) numerical solutions are made for various time steps. In particular we look at the accuracy of the ADM as the Lorenz system changes from a non-chaotic system to a chaotic one.

Original language	English
Pages (from-to)	1149-1158
Number of pages	10
Journal	Chaos, Solitons and Fractals
Volume	28
Issue number	5
DOIs	https://doi.org/10.1016/j.chaos.2005.08.135
State	Published - Jun 2006
Externally published	Yes

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10.1016/j.chaos.2005.08.135

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title = "Accuracy of the Adomian decomposition method applied to the Lorenz system",

abstract = "In this paper, the Adomian decomposition method (ADM) is applied to the famous Lorenz system. The ADM yields an analytical solution in terms of a rapidly convergent infinite power series with easily computable terms. Comparisons between the decomposition solutions and the fourth-order Runge-Kutta (RK4) numerical solutions are made for various time steps. In particular we look at the accuracy of the ADM as the Lorenz system changes from a non-chaotic system to a chaotic one.",

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AU - Hashim, I.

AU - Noorani, M. S.M.

AU - Ahmad, R.

AU - Bakar, S. A.

AU - Ismail, E. S.

AU - Zakaria, A. M.

PY - 2006/6

Y1 - 2006/6

N2 - In this paper, the Adomian decomposition method (ADM) is applied to the famous Lorenz system. The ADM yields an analytical solution in terms of a rapidly convergent infinite power series with easily computable terms. Comparisons between the decomposition solutions and the fourth-order Runge-Kutta (RK4) numerical solutions are made for various time steps. In particular we look at the accuracy of the ADM as the Lorenz system changes from a non-chaotic system to a chaotic one.

AB - In this paper, the Adomian decomposition method (ADM) is applied to the famous Lorenz system. The ADM yields an analytical solution in terms of a rapidly convergent infinite power series with easily computable terms. Comparisons between the decomposition solutions and the fourth-order Runge-Kutta (RK4) numerical solutions are made for various time steps. In particular we look at the accuracy of the ADM as the Lorenz system changes from a non-chaotic system to a chaotic one.

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DO - 10.1016/j.chaos.2005.08.135

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JO - Chaos, Solitons and Fractals

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IS - 5

ER -

Accuracy of the Adomian decomposition method applied to the Lorenz system

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