Neuro-Swarm heuristic using interior-point algorithm to solve a third kind of multi-singular nonlinear system

Zulqurnain Sabir; Muhammad Asif Zahoor Raja; Aldawoud Kamal; Juan L.G. Guirao; Dac-Nhuong Le; Tareq Saeed; Mohamad Salama; Zulqurnain Sabir; Muhammad Asif Zahoor Raja; Aldawoud Kamal; Juan L.G. Guirao; Dac-Nhuong Le; Tareq Saeed; Mohamad Salama

doi:10.3934/mbe.2021268

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 5: 5285-5308. doi: 10.3934/mbe.2021268

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Neuro-Swarm heuristic using interior-point algorithm to solve a third kind of multi-singular nonlinear system

1.
Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan
2.
Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin 64002, Taiwan, China
3.
Department of Mathematics and Statistics, Mutah University Jordan
4.
Department of Applied Mathematics and Statistics, Technical University of Cartagena, Hospital de Marina 30203-Cartagena, Spain
5.
Institute of Research and Development, Duy Tan University, Danang 550000, Vietnam Faculty of Information Technology, Duy Tan University, Danang 550000, Vietnam
6.
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
7.
Department of Engineering, Applied Science University, Bahrian

Academic Editor: Weining Wu

Received: 11 March 2021 Accepted: 25 May 2021 Published: 15 June 2021

The purpose of the present work is to solve a third kind of multi-singular nonlinear system using the neuro-swarm computing solver based on the artificial neural networks (ANNs) optimized with the effectiveness of particle swarm optimization (PSO) maintained by a local search proficiency of interior-point algorithm (IPA), i.e., ANN-PSO-IPA. An objective function is designed using the continuous mapping of ANN for nonlinear multi-singular third order system of Emden-Fowler equations and optimization of fitness function carried out with the integrated strength of PSO-IPA. The motivation to design the ANN-PSO-IPA is to present a feasible, reliable and feasible framework to handle with such complicated nonlinear multi-singular third order system of Emden-Fowler model. The designed ANN-PSO-IPA is tested for three different nonlinear variants of the multi-singular third kind of Emden-Fowler system. The obtained numerical results on single/multiple executions of the designed ANN-PSO-IPA are used to endorse the precision, viability and reliability.
- nonlinear singular system,
- artificial neural networks,
- multi-singular,
- interior-point algorithm,
- statistical analysis,
- hybrid approach
Citation: Zulqurnain Sabir, Muhammad Asif Zahoor Raja, Aldawoud Kamal, Juan L.G. Guirao, Dac-Nhuong Le, Tareq Saeed, Mohamad Salama. Neuro-Swarm heuristic using interior-point algorithm to solve a third kind of multi-singular nonlinear system[J]. Mathematical Biosciences and Engineering, 2021, 18(5): 5285-5308. doi: 10.3934/mbe.2021268

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Abstract

The purpose of the present work is to solve a third kind of multi-singular nonlinear system using the neuro-swarm computing solver based on the artificial neural networks (ANNs) optimized with the effectiveness of particle swarm optimization (PSO) maintained by a local search proficiency of interior-point algorithm (IPA), i.e., ANN-PSO-IPA. An objective function is designed using the continuous mapping of ANN for nonlinear multi-singular third order system of Emden-Fowler equations and optimization of fitness function carried out with the integrated strength of PSO-IPA. The motivation to design the ANN-PSO-IPA is to present a feasible, reliable and feasible framework to handle with such complicated nonlinear multi-singular third order system of Emden-Fowler model. The designed ANN-PSO-IPA is tested for three different nonlinear variants of the multi-singular third kind of Emden-Fowler system. The obtained numerical results on single/multiple executions of the designed ANN-PSO-IPA are used to endorse the precision, viability and reliability.

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