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Design of a Computational Heuristic to Solve the Nonlinear Liénard Differential Model

Li Yan1, Zulqurnain Sabir2, Esin Ilhan3, Muhammad Asif Zahoor Raja4, Wei Gao5, Haci Mehmet Baskonus6,*

1 School of Engineering, Honghe University, Mengzi, 661199, China
2 Department of Mathematics and Statistics, Hazara University, Mansehra, 21300, Pakistan
3 Faculty of Engineering and Architecture, Kirsehir Ahi Evran University, Kirsehir, 40500, Turkey
4 Future Technology Research Center, National Yunlin University of Science and Technology, Yunlin, 64002, Taiwan
5 School of Information Science and Technology, Yunnan Normal University, Kunming, 650500, China
6 Department of Mathematics and Science Education, Faculty of Education, Harran University, Sanliurfa, 63500, Turkey

* Corresponding Author: Haci Mehmet Baskonus. Email:

Computer Modeling in Engineering & Sciences 2023, 136(1), 201-221.


In this study, the design of a computational heuristic based on the nonlinear Liénard model is presented using the efficiency of artificial neural networks (ANNs) along with the hybridization procedures of global and local search approaches. The global search genetic algorithm (GA) and local search sequential quadratic programming scheme (SQPS) are implemented to solve the nonlinear Liénard model. An objective function using the differential model and boundary conditions is designed and optimized by the hybrid computing strength of the GA-SQPS. The motivation of the ANN procedures along with GA-SQPS comes to present reliable, feasible and precise frameworks to tackle stiff and highly nonlinear differential models. The designed procedures of ANNs along with GA-SQPS are applied for three highly nonlinear differential models. The achieved numerical outcomes on multiple trials using the designed procedures are compared to authenticate the correctness, viability and efficacy. Moreover, statistical performances based on different measures are also provided to check the reliability of the ANN along with GA-SQPS.


Cite This Article

Yan, L., Sabir, Z., Ilhan, E., Asif, M., Gao, W. et al. (2023). Design of a Computational Heuristic to Solve the Nonlinear Liénard Differential Model. CMES-Computer Modeling in Engineering & Sciences, 136(1), 201–221.

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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