Neuro-evolution computing for nonlinear multi-singular system of third order Emden–Fowler equation

Sabir, Zulqurnain; Raja, Muhammad Asif Zahoor; Khalique, Chaudry Masood; Ünlü, Canan

doi:10.1016/j.matcom.2021.02.004

Cited by 45 publications

(16 citation statements)

References 41 publications

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“…Example 2: Consider a nonlinear novel SSO-PDS by taking the values of 1 2   and 12 4   in Eqs ( 16) and ( 17) is given as:…”

Section: Resultsmentioning

confidence: 99%

“…The singular systems have various applications in the mathematical and engineering areas. The ordinary differential systems have much significance due to the wide range of applications in scientific and engineering fields, e.g., chemical reactor systems, biological applications, astrophysics, nonlinear circuits, control-based optimization theory, theory of boundary layer and fluidics [1][2][3][4][5][6]. The present investigations are associated to the Emden-Fowler system (EFS) that is famous due to singularity.…”

Section: Introductionmentioning

confidence: 99%

“…Few well known applications of LES are the mathematical physics [17], electromagnetics [18], density profile of gaseous star [19], oscillating magnetic areas [20], quantum mechanical networks [21], isotropic state of continuous media [22], sublinear neutral span [23] and system of stellar structure [24]. A number of techniques have been proposed to solve such singular systems since their invention [25][26][27][28][29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

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Design of Artificial Neural Networks for the Novel Applications of the Sixth Order Singular Nonlinear Pantograph Engineering Model

Sabir

Ali

Raja

et al. 2021

Preprint

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This aim of this study is to design and numerically investigate a novel nonlinear singular sixth order (SSO) pantograph differential system (PDS), i.e., SSO-PDS along with its five categories. The design of the novel nonlinear SSO-PDS is presented using the concepts of the standard Emden-Fowler along with the pantograph differential system. The singular systems are applied in many engineering and mathematical applications, like inverse models and viscoelasticity systems. The shape factor, singular point and pantograph terms are provided for each category of the novel nonlinear SSO-PDS. The numerical investigations of the nonlinear SSO-PDS are presented through the artificial neural networks (ANNs) using the Levenberg-Marquardt backpropagation (LMB), i.e., ANNs-LMB. The proposed results have been compared with the reference solutions to check the correctness of the designed novel model. The proposed solutions of the novel SSO-PDS are assessed using the training, testing and verification procedures in the form of mean square error (MSE). For the capability, efficacy and accuracy of the novel SSO-PDS through the ANNs, the numerical results are drawn using the MSE, error histograms and regression as well as correlation graphs.

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“…Example 2: Consider a nonlinear novel SSO-PDS by taking the values of 1 2   and 12 4   in Eqs ( 16) and ( 17) is given as:…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Design of Artificial Neural Networks for the Novel Applications of the Sixth Order Singular Nonlinear Pantograph Engineering Model

Sabir

Ali

Raja

et al. 2021

Preprint

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“…In future, the accessible MWNN-GA-ASA is promoted to solve the singular higher order, fractional models, smart cities model, and fluid dynamics systems [126][127][128][129][130][131][132][133][134][135][136][137][138][139][140][141][142][143].…”

Section: Acknowledgmentmentioning

confidence: 99%

IoT Technology Enabled Heuristic Model With Morlet Wavelet Neural Network for Numerical Treatment of Heterogeneous Mosquito Release Ecosystem

Sabir

Nisar²,

Raja

et al. 2021

IEEE Access

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The utmost advancements of artificial neural networks (ANNs), software-defined networks (SDNs) and internet of things (IoT) technologies find beneficial in different applications of the smart healthcare sector. Aiming at modern technology's use in the future development of healthcare, this paper presents an advanced heuristic based on Morlet wavelet neural network for solving the mosquito release ecosystem in a heterogeneous atmosphere. The mosquito release ecosystem is dependent of six classes, eggs density, larvae density, pupae density, mosquitoes searching for hosts density, resting mosquito's density and mosquitoes searching for ovipositional site density. An artificial neural network with the layer structure of Morlet wavelet (MWNN) kernel is presented using the global and local search optimization schemes of genetic algorithm (GA) and active-set algorithm (ASA), i.e., MWNN-GA-ASA. The accurateness, reliability and constancy of the proposed MWNN-GA-ASA is established through comparative examinations with Adams method based numerical results to solve the proposed nonlinear system with matching of order 10 -06 to 10 -09 . The accuracy and convergence of the proposed MWNN-GA-ASA is certified using the statistical operators based on root mean square error (RMSE), Theil's inequality coefficient (T.I.C) and mean absolute deviation (MAD) operators.INDEX TERMS Mosquito release ecosystem, IoT, SDN, artificial neural networks, heuristic algorithm, Adams's method.

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“…Stochastic approaches are efficient to solve many complex models using the swarming/evolutionary approaches such as singular higher order models [18][19][20][21], dusty plasma models [22], functional singular differential systems [23,24], biological models [25][26][27][28], fluid dynamic problems [29][30][31], singular Lane-Emden model [32,33], electric circuits [34,35], Thomas-Fermi singular model [36], singular three-point model [37] and periodic differential model [38]. The potential visualizations of the proposed LMB neural network are provided as:…”

Section: Introductionmentioning

confidence: 99%

Computational Intelligent Paradigms to Solve the Nonlinear SIR System for Spreading Infection and Treatment Using Levenberg–Marquardt Backpropagation

et al. 2021

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The current study aims to design an integrated numerical computing-based scheme by applying the Levenberg–Marquardt backpropagation (LMB) neural network to solve the nonlinear susceptible (S), infected (I) and recovered (R) (SIR) system of differential equations, representing the spreading of infection along with its treatment. The solutions of both the categories of spreading infection and its treatment are presented by taking six different cases of SIR models using the designed LMB neural network. A reference dataset of the designed LMB neural network is established with the Adam numerical scheme for each case of the spreading infection and its treatment. The approximate outcomes of the SIR system based on the spreading infection and its treatment are presented in the training, authentication and testing procedures to adapt the neural network by reducing the mean square error (MSE) function using the LMB. Studies based on the proportional performance and inquiries based on correlation, error histograms, regression and MSE results establish the efficiency, correctness and effectiveness of the proposed LMB neural network scheme.

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Neuro-evolution computing for nonlinear multi-singular system of third order Emden–Fowler equation

Cited by 45 publications

References 41 publications

Design of Artificial Neural Networks for the Novel Applications of the Sixth Order Singular Nonlinear Pantograph Engineering Model

Design of Artificial Neural Networks for the Novel Applications of the Sixth Order Singular Nonlinear Pantograph Engineering Model

IoT Technology Enabled Heuristic Model With Morlet Wavelet Neural Network for Numerical Treatment of Heterogeneous Mosquito Release Ecosystem

Computational Intelligent Paradigms to Solve the Nonlinear SIR System for Spreading Infection and Treatment Using Levenberg–Marquardt Backpropagation

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