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AIMS Mathematics

2021, Volume 6, Issue 3: 2468-2485. doi: 10.3934/math.2021150
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Research article

Neuro-swarms intelligent computing using Gudermannian kernel for solving a class of second order Lane-Emden singular nonlinear model

  • 1.
    Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan
  • 2.
    Future Research Technology Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin 64002, Taiwan, R.O.C
  • 3.
    Department of Computer and Electrical Engineering, COMSATS University Islamabad, Attock Campus, Attock 43600, Pakistan
  • 4.
    Department of Advanced Sciences and Technologies at National School of Advanced Sciences and Technologies of Borj Cedria; Laboratory of Engineering Mathematics (LR01ES13), Tunisia Polytechnic School, University of Carthage, Tunisia
  • 5.
    Department of General Studies, National Autonomous University of Chota, Perú
  • 6.
    School of Mathematics, Southeast University, Nanjing, China
  • 7.
    Yonsei Frontier Lab, Yonsei University, Seoul, Korea
  • Received: 27 September 2020 Accepted: 09 December 2020 Published: 21 December 2020

  • MSC : 68T20, 65Lxx, 68U99

  • The present work is to design a novel Neuro swarm computing standards using artificial intelligence scheme to exploit the Gudermannian neural networks (GNN)accomplished with global and local search ability of particle swarm optimization (PSO) and sequential quadratic programming scheme (SQPS), called as GNN-PSO-SQPS to solve a class of the second order Lane-Emden singular nonlinear model (SO-LES-NM). The suggested intelligent computing solver GNN-PSO-SQPS using the Gudermannian kernel are unified with the configuration of the hidden layers of GNN of differential operators for solving the SO-LES-NM. An error based fitness function (FF) applying the differential form of the differential model and corresponding boundary conditions. The FF is optimized together with the combined heuristics of PSO-SQPS. Three problems of the SO-LES-NM are solved to validate the correctness, effectiveness and competence of the designed GNN-PSO-SQPS. The performance of the GNN-PSO-SQPS through statistical operators is tested to check the constancy, convergence and precision.

    Citation: Zulqurnain Sabir, Muhammad Asif Zahoor Raja, Adnène Arbi, Gilder Cieza Altamirano, Jinde Cao. Neuro-swarms intelligent computing using Gudermannian kernel for solving a class of second order Lane-Emden singular nonlinear model[J]. AIMS Mathematics, 2021, 6(3): 2468-2485. doi: 10.3934/math.2021150

    Related Papers:

  • The present work is to design a novel Neuro swarm computing standards using artificial intelligence scheme to exploit the Gudermannian neural networks (GNN)accomplished with global and local search ability of particle swarm optimization (PSO) and sequential quadratic programming scheme (SQPS), called as GNN-PSO-SQPS to solve a class of the second order Lane-Emden singular nonlinear model (SO-LES-NM). The suggested intelligent computing solver GNN-PSO-SQPS using the Gudermannian kernel are unified with the configuration of the hidden layers of GNN of differential operators for solving the SO-LES-NM. An error based fitness function (FF) applying the differential form of the differential model and corresponding boundary conditions. The FF is optimized together with the combined heuristics of PSO-SQPS. Three problems of the SO-LES-NM are solved to validate the correctness, effectiveness and competence of the designed GNN-PSO-SQPS. The performance of the GNN-PSO-SQPS through statistical operators is tested to check the constancy, convergence and precision.


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