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A novel design of a sixth-order nonlinear modeling for solving engineering phenomena based on neuro intelligence algorithm

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Abstract

The current study aims to present a novel design of a sixth-order (SO) nonlinear Emden–Fowler nonlinear system (SO-NSEFM) along with its five types. The novel design of SO-NSEFM is achieved using the typical second-order Emden–Fowler system. The detail of the singularity and shape factors is presented for each type of the SO-NSEFM. Three different examples of each type of the designed SO-NSEFM will be solved using the supervised neural network (SNN) Levenberg–Marquardt backpropagation approach (LMBA), i.e., SNN–LMBA. A reference dataset using the spectral collocation scheme with the proposed SNN–LMBA will be established for the designed SO-NSEFM. The achieved approximate outcomes of the designed SO-NSEFM are accessible using the procedures of testing, verification, and training of the proposed neural networks to reduce the MSE. For the efficiency, correctness, and effectiveness of the proposed SNN-LMBA, the investigations are presented through the proportional performances of regression, MSE results, correlation and error histograms (EHs), and regression.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan

    Zulqurnain Sabir

  2. Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin, 64002, Taiwan, ROC

    Muhammad Asif Zahoor Raja

  3. Department of Mathematics, COMSATS University Islamabad, Attock Campus, Attock, 43600, Pakistan

    Muhammad Shoaib

  4. Department of Mathematics, Zagazig Faculty of Engineering, Zagazig University, Zagazig, Egypt

    R. Sadat

  5. Faculty of Engineering and Technology, Future University, Cairo, Egypt

    Mohamed R. Ali

  6. Department of Basic Science, Faculty of Engineering at Benha, Benha University, Banha, 13512, Egypt

    Mohamed R. Ali

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  1. Zulqurnain Sabir
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  2. Muhammad Asif Zahoor Raja
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  3. Muhammad Shoaib
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  4. R. Sadat
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  5. Mohamed R. Ali
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Correspondence to Mohamed R. Ali.

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Sabir, Z., Raja, M.A.Z., Shoaib, M. et al. A novel design of a sixth-order nonlinear modeling for solving engineering phenomena based on neuro intelligence algorithm. Engineering with Computers 39, 1807–1822 (2023). https://doi.org/10.1007/s00366-021-01596-0

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