Heuristic computing technique for numerical solutions of nonlinear fourth order Emden–Fowler equation

Sabir, Zulqurnain; Saoud, Sahar; Raja, Muhammad Asif Zahoor; Wahab, Hafiz Abdul; Arbi, Adnène

doi:10.1016/j.matcom.2020.06.021

Cited by 97 publications

(36 citation statements)

References 55 publications

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“…In the future, the proposed scheme ANN-GA-ASM can be applied as an accurate and efficient stochastic numerical solver for nonlinear singular models [42][43][44], computational models of fluid dynamics [45][46][47][48], fractional models [49][50][51][52], and biological models [53][54][55][56][57].…”

Section: Resultsmentioning

confidence: 99%

Design and Numerical Solutions of a Novel Third-Order Nonlinear Emden–Fowler Delay Differential Model

Guirao

Sabir

Saeed

2020

Mathematical Problems in Engineering

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In this study, the design of a novel model based on nonlinear third-order Emden–Fowler delay differential (EF-DD) equations is presented along with two types using the sense of delay differential and standard form of the second-order EF equation. The singularity at ξ = 0 at single or multiple points of each type of the designed EF-DD model are discussed. The detail of shape factors and delayed points is provided for both types of the designed third-order EF-DD model. For the verification and validation of the model, two numerical examples are presented of each case and numerical results have been performed using the artificial neural network along with the hybrid of global and local capabilities. The comparison of the obtained numerical results with the exact solutions shows the perfection and correctness of the designed third-order EF-DD model.

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Section: Resultsmentioning

confidence: 99%

Design and Numerical Solutions of a Novel Third-Order Nonlinear Emden–Fowler Delay Differential Model

Guirao

Sabir

Saeed

2020

Mathematical Problems in Engineering

Self Cite

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“…It can be applied to optimize both constrained and unconstrained types of problems. Recently, GA is applied in many famous applications of heart diagnosis system [42], nonlinear electric circuit models [43], nonlinear astrophysics based singular system [44], Painlevé equation-II based nonlinear optic models [45], prediction model of air blast [46], Thomas Fermi model [47], and monorail vehicle system [48]. These potential applications of GA inspired the authors to solve the singular pantograph differential model to attain the decision variables of MWNNs.…”

Section: B Optimization Process: Gaipamentioning

confidence: 99%

Design of Morlet Wavelet Neural Network for Solving a Class of Singular Pantograph Nonlinear Differential Models

et al. 2021

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The aim of this study is to design a layer structure of feed-forward artificial neural networks using the Morlet wavelet activation function for solving a class of pantograph differential Lane-Emden models. The Lane-Emden pantograph differential equation is one of the important kind of singular functional differential model. The numerical solutions of the singular pantograph differential model are presented by the approximation capability of the Morlet wavelet neural networks (MWNNs) accomplished with the strength of global and local search terminologies of genetic algorithm (GA) and interior-point algorithm (IPA), i.e., MWNN-GAIPA. Three different problems of the singular pantograph differential models have been numerically solved by using the optimization procedures of MWNN-GAIPA. The correctness of the designed MWNN-GAIPA is observed by comparing the obtained results with the exact solutions. The analysis for 3, 6 and 60 neurons are also presented to check the stability and performance of the designed scheme. Moreover, different statistical analysis using forty number of trials is presented to check the convergence and accuracy of the proposed MWNN-GAIPA scheme.

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“…All presented above schemes have their individual sensitivity, potential, efficiency, and correctness, as well as weaknesses, flaws, and demerits over each other. The extensive computing heuristic approach potential is to solve the singular systems applying the widespread capacity of artificial neural networks (ANNs) collectively with local and global based search approaches [17][18][19][20][21][22][23]. Few noteworthy illustrations contain neuro-intelligent computing approach to study the dynamics of convective heat transfer involving carbon nanotubes [24], dusty plasma nonlinear model [25], model of mosquito release in the heterogeneous atmosphere [26], Navier Stokes problems [27], singular functional differential model [28], HIV infection system of CD4+ T cells [29], plasma-based physics investigations [30], Thomas-Fermi singular system [31], prey-predator biological system [32], nanotechnology [33], killing well control system [34], biological model based on corneal shape [35], Jeffery Hamel flow problem [36], parameter estimation in biodiesel studies [37] and model of atomic physics model [38].…”

Section: Introductionmentioning

confidence: 99%

Evolutionary Integrated Heuristic with Gudermannian Neural Networks for Second Kind of Lane–Emden Nonlinear Singular Models

et al. 2021

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In this work, a new heuristic computing design is presented with an artificial intelligence approach to exploit the models with feed-forward (FF) Gudermannian neural networks (GNN) accomplished with global search capability of genetic algorithms (GA) combined with local convergence aptitude of active-set method (ASM), i.e., FF-GNN-GAASM to solve the second kind of Lane–Emden nonlinear singular models (LE-NSM). The proposed method based on the computing intelligent Gudermannian kernel is incorporated with the hidden layer configuration of FF-GNN models of differential operatives of the LE-NSM, which are arbitrarily associated with presenting an error-based objective function that is used to optimize by the hybrid heuristics of GAASM. Three LE-NSM-based examples are numerically solved to authenticate the effectiveness, accurateness, and efficiency of the suggested FF-GNN-GAASM. The reliability of the scheme via statistical valuations is verified in order to authenticate the stability, accuracy, and convergence.

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Heuristic computing technique for numerical solutions of nonlinear fourth order Emden–Fowler equation

Cited by 97 publications

References 55 publications

Design and Numerical Solutions of a Novel Third-Order Nonlinear Emden–Fowler Delay Differential Model

Design and Numerical Solutions of a Novel Third-Order Nonlinear Emden–Fowler Delay Differential Model

Design of Morlet Wavelet Neural Network for Solving a Class of Singular Pantograph Nonlinear Differential Models

Evolutionary Integrated Heuristic with Gudermannian Neural Networks for Second Kind of Lane–Emden Nonlinear Singular Models

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