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An optimized decomposition method for nonlinear ordinary and partial differential equations

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  • Odibat, Zaid

Abstract

In this paper, firstly, an innovative decomposition method, called the optimized decomposition method, is suggested to analytically solve nonlinear ODEs. The proposed technique designs a new optimal construction of the series solutions based on a linear approximation of the nonlinear equation. Then, an efficient adaptation of the optimized decomposition method that will expand the application of the method to nonlinear PDEs is developed. Actual comparison between the suggested method and the Adomian decomposition method is carried out through numerical simulation of some test problems. The study demonstrates that the proposed method works successfully in dealing with nonlinear differential equations and gives better accuracy and convergence compared to Adomian decomposition method. The new proposed method reported in this work is believed to be implemented more widely to handle nonlinear models in applied sciences.

Suggested Citation

  • Odibat, Zaid, 2020. "An optimized decomposition method for nonlinear ordinary and partial differential equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    • Handle: RePEc:eee:phsmap:v:541:y:2020:i:c:s0378437119318618
    DOI: 10.1016/j.physa.2019.123323
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    References listed on IDEAS

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    1. Momani, Shaher & Odibat, Zaid, 2007. "Numerical comparison of methods for solving linear differential equations of fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1248-1255.
    2. El-Wakil, S.A. & Abdou, M.A., 2007. "New applications of Adomian decomposition method," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 513-522.
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    Cited by:

    1. Mondal, Argha & Mistri, Kshitish Ch. & Aziz-Alaoui, M.A. & Upadhyay, Ranjit Kumar, 2021. "An analytical scheme on complete integrability of 2D biophysical excitable systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).
    2. Kaushik, Sonali & Kumar, Rajesh, 2023. "Optimized decomposition method for solving multi-dimensional Burgers’ equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 326-350.

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