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Integrated intelligent computing with neuro-swarming solver for multi-singular fourth-order nonlinear Emden–Fowler equation

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Abstract

In the present work, a novel neuro-swarming based heuristic solver is established for the numerical solutions of fourth-order multi-singular nonlinear Emden–Fowler (FO-MS-NEF) model using the function estimate capability of artificial neural networks (ANNs) modelling together with the global application of particle swarm optimization (PSO) enhanced by local search active set (AS) approach, i.e., ANN-PSO-AS solver. The design stimulation for the ANN-PSO-AS scheme for a numerical solver originates with an intention to present a viable, consistent and precise configuration that associates the ANNs strength under the optimization of unified soft computing backgrounds to tackle with such stimulating models for the FO-MS-NEF equation. The proposed ANN-PSO-AS solver is applied for three different variants of FO-MS-NEF equations. The comparison of the obtained results with the true solutions calmed its correctness, effectiveness, and robustness that is further validated with in-depth statistical investigations.

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Acknowledgements

This study was funded by Ministerio de Ciencia, Innovación y Universidades (grant number PGC2018-0971-B-100), Fundación Séneca (Grant number 20783/PI/18).

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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, R.O.C.

    Muhammad Asif Zahoor Raja

  3. Department of Electrical and Computer Engineering, COMSATS University Islamabad, Attock Campus, Attock, 43600, Pakistan

    Muhammad Asif Zahoor Raja

  4. Department of Applied Mathematics and Statistics, Technical University of Cartagena, Hospital de Marina, 30203, Cartagena, Spain

    Juan L. G. Guirao

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

    Muhammad Shoaib

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  1. Zulqurnain Sabir
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  2. Muhammad Asif Zahoor Raja
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  3. Juan L. G. Guirao
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  4. Muhammad Shoaib
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Correspondence to Juan L. G. Guirao.

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Communicated by Marcos Eduardo Valle.

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Sabir, Z., Raja, M.A.Z., Guirao, J.L.G. et al. Integrated intelligent computing with neuro-swarming solver for multi-singular fourth-order nonlinear Emden–Fowler equation . Comp. Appl. Math. 39, 307 (2020). https://doi.org/10.1007/s40314-020-01330-4

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