Solving a new design of nonlinear second-order Lane–Emden pantograph delay differential model via Bernoulli collocation method

Adel, Waleed; Sabir, Zulqurnain

doi:10.1140/epjp/s13360-020-00449-x

Cited by 85 publications

(45 citation statements)

References 45 publications

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“…e single singularity at ξ � 0 has been noticed in the above equation (13). e shape factor is k and delayed expression appears twice in the above equation.…”

Section: Type 2 Equation (mentioning

confidence: 84%

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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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“…e single singularity at ξ � 0 has been noticed in the above equation (13). e shape factor is k and delayed expression appears twice in the above equation.…”

Section: Type 2 Equation (mentioning

confidence: 84%

“…Erdogan et al [11] implemented finite difference approach on layer-adapted mesh using the singularly perturbed DD equations. e general form of the DD model is written as [12,13]…”

Section: Introductionmentioning

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

View full text Add to dashboard Cite

show abstract

“…Solving the singular models is found to be grim and tough due to a singular point at the origin. Few analytical and numerical schemes are accessible to handle such singular nonlinear models are presented in these references [14][15][16].…”

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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“…Some well-known submissions are HIV infection model [33], nonlinear Bratu's systems [34], heat conduction dynamics based on singular nonlinear human head model [35], singular three-point model [36], Thomas-Fermi model [37], multi-singular nonlinear models [38], model of heartbeat dynamics [39], singular periodic model [40], prey-predator models [41] and nonlinear singular functional differential model [42,43]. The generic form of the NSO-LE-MPDD model is shown as [44]:…”

Section: Introductionmentioning

confidence: 99%

A neuro-swarming intelligent heuristic for second-order nonlinear Lane–Emden multi-pantograph delay differential system

Sabir

Raja

et al. 2021

Complex Intell. Syst.

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The current study is related to present a novel neuro-swarming intelligent heuristic for nonlinear second-order Lane–Emden multi-pantograph delay differential (NSO-LE-MPDD) model by applying the approximation proficiency of artificial neural networks (ANNs) and local/global search capabilities of particle swarm optimization (PSO) together with efficient/quick interior-point (IP) approach, i.e., ANN-PSOIP scheme. In the designed ANN-PSOIP scheme, a merit function is proposed by using the mean square error sense along with continuous mapping of ANNs for the NSO-LE-MPDD model. The training of these nets is capable of using the integrated competence of PSO and IP scheme. The inspiration of the ANN-PSOIP approach instigates to present a reliable, steadfast, and consistent arrangement relates the ANNs strength for the soft computing optimization to handle with such inspiring classifications. Furthermore, the statistical soundings using the different operators certify the convergence, accurateness, and precision of the ANN-PSOIP scheme.

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Solving a new design of nonlinear second-order Lane–Emden pantograph delay differential model via Bernoulli collocation method

Cited by 85 publications

References 45 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

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

A neuro-swarming intelligent heuristic for second-order nonlinear Lane–Emden multi-pantograph delay differential system

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