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On accuracy of Adomian decomposition method for hyperchaotic Rössler system

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  • Al-Sawalha, M. Mossa
  • Noorani, M.S.M.
  • Hashim, I.

Abstract

The aim of this paper is to investigate the accuracy of the Adomian decomposition method for solving the hyperchaotic Rössler system, which is a four-dimensional system of ODEs with quadratic nonlinearities. Comparisons between the decomposition solutions and the fourth-order Runge–Kutta (RK4) solutions are made. It is found that the comparable accuracy of the ADM with the RK4 for the chaotic Lorenz system does not carry to the hyperchaotic Rössler system.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:4:p:1801-1807
    DOI: 10.1016/j.chaos.2007.09.062
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    References listed on IDEAS

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    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. Zhang, Hao & Ma, Xi-kui & Li, Ming & Zou, Jian-long, 2005. "Controlling and tracking hyperchaotic Rössler system via active backstepping design," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 353-361.
    3. 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.
    4. 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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    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. 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.
    3. 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.
    4. 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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