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Accuracy of the Adomian decomposition method applied to the Lorenz system

Author

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

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.

Suggested Citation

  • Hashim, I. & Noorani, M.S.M. & Ahmad, R. & Bakar, S.A. & Ismail, E.S. & Zakaria, A.M., 2006. "Accuracy of the Adomian decomposition method applied to the Lorenz system," Chaos, Solitons & Fractals, Elsevier, vol. 28(5), pages 1149-1158.
    • Handle: RePEc:eee:chsofr:v:28:y:2006:i:5:p:1149-1158
    DOI: 10.1016/j.chaos.2005.08.135
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    Citations

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    Cited by:

    1. Noorani, M.S.M. & Hashim, I. & Ahmad, R. & Bakar, S.A. & Ismail, E.S. & Zakaria, A.M., 2007. "Comparing numerical methods for the solutions of the Chen system," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1296-1304.
    2. Alexander N. Pchelintsev, 2022. "On a High-Precision Method for Studying Attractors of Dynamical Systems and Systems of Explosive Type," Mathematics, MDPI, vol. 10(8), pages 1-12, April.
    3. Abdel-Halim Hassan, I.H., 2008. "Comparison differential transformation technique with Adomian decomposition method for linear and nonlinear initial value problems," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 53-65.
    4. Chowdhury, M.S.H. & Hashim, I. & Momani, S., 2009. "The multistage homotopy-perturbation method: A powerful scheme for handling the Lorenz system," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1929-1937.
    5. Abdulaziz, O. & Noor, N.F.M. & Hashim, I. & Noorani, M.S.M., 2008. "Further accuracy tests on Adomian decomposition method for chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1405-1411.
    6. Mossa Al-sawalha, M. & Noorani, M.S.M., 2009. "A numeric–analytic method for approximating the chaotic Chen system," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1784-1791.
    7. Memarbashi, Reza, 2008. "Numerical solution of the Laplace equation in annulus by Adomian decomposition method," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 138-143.
    8. Dehghan, Mehdi & Shakourifar, Mohammad & Hamidi, Asgar, 2009. "The solution of linear and nonlinear systems of Volterra functional equations using Adomian–Pade technique," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2509-2521.
    9. Hashim, I. & Chowdhury, M.S.H. & Mawa, S., 2008. "On multistage homotopy-perturbation method applied to nonlinear biochemical reaction model," Chaos, Solitons & Fractals, Elsevier, vol. 36(4), pages 823-827.
    10. Goh, S.M. & Noorani, M.S.M. & Hashim, I., 2009. "Efficacy of variational iteration method for chaotic Genesio system – Classical and multistage approach," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2152-2159.
    11. Sekson Sirisubtawee & Supaporn Kaewta, 2017. "New Modified Adomian Decomposition Recursion Schemes for Solving Certain Types of Nonlinear Fractional Two-Point Boundary Value Problems," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2017, pages 1-20, July.
    12. Lozi, René & Pogonin, Vasiliy A. & Pchelintsev, Alexander N., 2016. "A new accurate numerical method of approximation of chaotic solutions of dynamical model equations with quadratic nonlinearities," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 108-114.
    13. Al-Sawalha, M. Mossa & Noorani, M.S.M. & Hashim, I., 2009. "On accuracy of Adomian decomposition method for hyperchaotic Rössler system," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1801-1807.
    14. Goh, S.M. & Noorani, M.S.M. & Hashim, I., 2009. "A new application of variational iteration method for the chaotic Rössler system," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1604-1610.

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