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Neuron Analysis of the Two-Point Singular Boundary Value Problems Arising in the Thermal Explosion’s Theory

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Abstract

The purpose of the present study is to present the neuron analysis using the unsupervised artificial neural networks (US-ANNs) for solving a class of two-point nonlinear singular boundary value problems (TPN-SBVPs) arising in the thermal explosion’s theory. The analysis using small and large neurons (3, 10 and 30 neurons) is presented along with the absolute error performances and complexity cost. An error function is optimized using the global and local search mechanisms called genetic algorithm (GA) and active-set approach (ASA) for solving the TPN-SBVPs. The correctness of the designed scheme US-ANNs using the hybrid combination of GA-ASA is approved through the comparison of obtained and true solutions. Moreover, statistical analysis will also be performed to authenticate the reliability and competency of the proposed method for solving the singular model.

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Authors and Affiliations

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

    Zulqurnain Sabir & Hafiz Abdul Wahab

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

    Mohamed R. Ali

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

    Mohamed R. Ali

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

    R. Sadat

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  1. Zulqurnain Sabir
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  2. Hafiz Abdul Wahab
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  3. Mohamed R. Ali
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  4. R. Sadat
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Correspondence to Mohamed R. Ali.

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Sabir, Z., Wahab, H.A., Ali, M.R. et al. Neuron Analysis of the Two-Point Singular Boundary Value Problems Arising in the Thermal Explosion’s Theory. Neural Process Lett 54, 4297–4324 (2022). https://doi.org/10.1007/s11063-022-10809-6

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