The present study shows an intelligence computational framework for solving the singular, linear, and nonlinear Emden-Fowler models using the well-known artificial neural networks (ANNs), genetic algorithm is a global search scheme, interior-point is a capable local search scheme and the hybrid of local and global search schemes. The neural network methods designate the suitable approaches to attain valuable prototypes using the unsubstantiated error for solving the singular models. The incentive to award this research is to originate a consistent framework combines with the significant topographies of ANNs to tackle the challenges of the singular systems. Comprehensive numerical research is proficient to approve the robustness, convergence, and correctness of the proposed numerical approach. The numerical measures are also compared with the true solutions to authenticate the excellence of the proposed numerical scheme.

Keywords: Nonlinear; Singular systems; Genetic algorithm; Interior-point scheme; Hybridization

References

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[4] C.M. Bender, K.A. Milton, S.S. Pinsky and Jr. L.M. Simmons, A new perturbative approach to nonlinear problems, Journal of Mathematics and Physics 30 (1989), 1447-1455.

Affliation: 

1Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan 
2Department of Mathematical Sciences, United Arab Emirates University, P. O. Box 15551, Al Ain, UAE.

Zulqurnain Sabir is native of a small village Pothi, district Jhelum, Pakistan. He has completed his MSc degree in Mathematics from Punjab University, Lahore, Pakistan. He passed M. Phil in mathematics from Preston University Kohat, Islamabad Campus, Pakistan. He graduated his PhD mathematics from the Hazara University, Mansehra, Pakistan. He has published more than 170 research papers in reported international WoS journals with good impact factor. His cumulative impact factor is more than 520, with 36 h-index and 90 i10- index. His area of interests includes artificial intelligence, mathematical modeling, unsupervised/supervised neural networks, deep neural networks, and implementation of computational based traditional as well as heuristic techniques. He is famous to solve the singular nonlinear models, functional models, fractional models, higher order, biological models, and fluid models. He is a pioneer to extend Lane-Emden and Emden-Fowler models up to 3rd, 4th, 5th, 6th, 7th order and solved competently by applying the artificial neural networks. He also solved the second order pantograph, prediction, and delay differential singular models. He worked to solve the fractional order differential biological models with the recent applications of SITR model based on coronavirus, dynamics of the bone transformation, nervous stomach, HIV, cancer model, waterborne spread and control of diseases, influenza disease mathematical model, Leptospirosis model, dengue model, etc. Recently, he is nominated in the list of top 2% of scientists with various disciplines according to Stanford University global list. He is currently working as a senior researcher in the United Arab Emirates University, Al Ain, UAE.