Accuracy of the Adomian decomposition method applied to the Lorenz system

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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 languageEnglish
Pages (from-to)1149-1158
Number of pages10
JournalChaos, Solitons and Fractals
Volume28
Issue number5
DOIs
Publication statusPublished - Jun 2006

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Adomian Decomposition Method
Lorenz System
decomposition
Infinite series
Runge-Kutta
Power series
Fourth Order
Analytical Solution
power series
Numerical Solution
Decompose
Term

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics

Cite this

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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.",
author = "Ishak Hashim and {Md. Noorani}, {Mohd. Salmi} and Ahmad, {Rokiah @ Rozita} and {Abu Bakar}, Sakhinah and Ismail, {Eddie Shahril} and Zakaria, {A. M.}",
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AU - Hashim, Ishak

AU - Md. Noorani, Mohd. Salmi

AU - Ahmad, Rokiah @ Rozita

AU - Abu Bakar, Sakhinah

AU - Ismail, Eddie Shahril

AU - Zakaria, A. M.

PY - 2006/6

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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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