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Further accuracy tests on Adomian decomposition method for chaotic systems

Author

Listed:
  • Abdulaziz, O.
  • Noor, N.F.M.
  • Hashim, I.
  • Noorani, M.S.M.

Abstract

The Adomian decomposition method (ADM) is treated as an algorithm for approximating the solutions of the Lorenz and Chen systems in a sequence of time intervals, i.e. the classical ADM is converted into a hybrid analytical–numerical method. Comparisons with the seventh- and eighth-order Runge–Kutta method (RK78) reconfirm the very high accuracy of the hybrid analytical–numerical ADM.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:36:y:2008:i:5:p:1405-1411
    DOI: 10.1016/j.chaos.2006.09.007
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    1. 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.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.

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