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Swarming Computational Efficiency to Solve a Novel Third-Order Delay Differential Emden-Fowler System

Wajaree Weera1, Zulqurnain Sabir2, Muhammad Asif Zahoor Raja3, Sakda Noinang4, Thongchai Botmart1,*

1 Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen, 40002, Thailand
2 Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan
3 Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section  3, Douliou, Yunlin, 64002, Taiwan
4 Department of Mathematics Statistics and Computer, Faculty of Science, Ubon Ratchathani University, Ubon Ratchathani, 34190, Thailand

* Corresponding Author: Thongchai Botmart. Email:

Computers, Materials & Continua 2022, 73(3), 4833-4849.


The purpose of this research is to construct an integrated neuro swarming scheme using the procedures of the artificial neural networks (ANNs) with the use of global search particle swarm optimization (PSO) along with the competent local search interior-point programming (IPP) called as ANN-PSOIPP. The proposed computational scheme is implemented for the numerical simulations of the third order nonlinear delay differential Emden-Fowler model (TON-DD-EFM). The TON-DD-EFM is based on two types along with the particulars of shape factor, delayed terms, and singular points. A merit function is performed using the optimization of PSOIPP to find the solutions to the TON-DD-EFM. The effectiveness of the ANN-PSOIPP is certified through the comparison with the exact results for solving four examples of the TON-DD-EFM. The scheme’s efficiency is observed by performing the absolute error in suitable measures found around 10−04 to 10−07. Furthermore, the statistical-based assessments for 100 trials are provided to compute the accuracy, stability, and constancy of the ANN-PSOIPP for solving the TON-DD-EFM.


Cite This Article

W. Weera, Z. Sabir, M. A. Zahoor Raja, S. Noinang and T. Botmart, "Swarming computational efficiency to solve a novel third-order delay differential emden-fowler system," Computers, Materials & Continua, vol. 73, no.3, pp. 4833–4849, 2022.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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