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A hybrid Harris hawks-Nelder-Mead optimization for practical nonlinear ordinary differential equations

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Abstract

Differential equations can often be seen in many fields of scientific research and engineering. Typically, finding the analytical (exact) solution is expensive task in terms of computational effort and may not an attainable task for some complex tasks. To effectively handle a wide variety of linear and nonlinear differential equations, this paper presents an approximate methodology based on hybrid Harris hawks–Nelder–Mead optimization algorithm with the aim to achieve accurate and reliable solution. The proposed methodology is introduced on basis of Fourier series expansion and Harris hawks–Nelder–Mead optimization algorithm. In this sense, the differential equation is represented as an optimization model by the means of the weighted residual function (cost function) that needed to be minimized, where the boundary and initial conditions of the differential equation are considered as the constraints of the optimization model. The practicality and efficiency of the proposed algorithm are demonstrated through six differential equations with different nature as well as four mechanical engineering differential equations. The comparison against different algorithms, by using the generational distance metric and Wilcoxon sign rank test, showed the effectiveness of the proposed algorithm.

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Authors and Affiliations

  1. Faculty of Engineering, Menoufia University, Shebin El-Kom, Egypt

    Rizk M. Rizk-Allah

  2. Faculty of Computers and Information, Cairo University, Giza, Egypt

    Aboul Ella Hassanien

  3. Scientific Research Group in Egypt (SRGE) http://www.egyptscience.net

    Rizk M. Rizk-Allah & Aboul Ella Hassanien

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  1. Rizk M. Rizk-Allah
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  2. Aboul Ella Hassanien
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Correspondence to Aboul Ella Hassanien.

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Rizk M. Rizk-Allah, Aboul Ella Hassanien: Scientific Research Group in Egypt http://www.egyptscience.net.

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Rizk-Allah, R.M., Hassanien, A.E. A hybrid Harris hawks-Nelder-Mead optimization for practical nonlinear ordinary differential equations. Evol. Intel. 15, 141–165 (2022). https://doi.org/10.1007/s12065-020-00497-3

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  • DOI: https://doi.org/10.1007/s12065-020-00497-3

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