Design of a Novel Second-Order Prediction Differential Model Solved by Using Adams and Explicit Runge–Kutta Numerical Methods

Sabir, Zulqurnain; Guirao, Juan Luis García; Saeed, Tareq; Erdoğan, Fevzi

doi:10.1155/2020/9704968

Cited by 20 publications

(14 citation statements)

References 27 publications

(27 reference statements)

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“…In future research, the presented FF-ANN-GASQP scheme algorithm can be implemented as an efficient/accurate stochastic numerical solver for the nonlinear dynamical measures of a computational fluid mechanics model [46][47][48][49][50], renewed fractional order processing systems [51][52][53][54], higher-order singular models [55], parameter estimation problems and electromagnetic waves [56,57], a prediction differential model [58], and bioinformatics [59][60][61].…”

Section: Discussionmentioning

confidence: 99%

A Stochastic Intelligent Computing with Neuro-Evolution Heuristics for Nonlinear SITR System of Novel COVID-19 Dynamics

et al. 2020

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The present study aims to design stochastic intelligent computational heuristics for the numerical treatment of a nonlinear SITR system representing the dynamics of novel coronavirus disease 2019 (COVID-19). The mathematical SITR system using fractal parameters for COVID-19 dynamics is divided into four classes; that is, susceptible (S), infected (I), treatment (T), and recovered (R). The comprehensive details of each class along with the explanation of every parameter are provided, and the dynamics of novel COVID-19 are represented by calculating the solution of the mathematical SITR system using feed-forward artificial neural networks (FF-ANNs) trained with global search genetic algorithms (GAs) and speedy fine tuning by sequential quadratic programming (SQP)—that is, an FF-ANN-GASQP scheme. In the proposed FF-ANN-GASQP method, the objective function is formulated in the mean squared error sense using the approximate differential mapping of FF-ANNs for the SITR model, and learning of the networks is proficiently conducted with the integrated capabilities of GA and SQP. The correctness, stability, and potential of the proposed FF-ANN-GASQP scheme for the four different cases are established through comparative assessment study from the results of numerical computing with Adams solver for single as well as multiple autonomous trials. The results of statistical evaluations further authenticate the convergence and prospective accuracy of the FF-ANN-GASQP method.

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Section: Discussionmentioning

confidence: 99%

A Stochastic Intelligent Computing with Neuro-Evolution Heuristics for Nonlinear SITR System of Novel COVID-19 Dynamics

et al. 2020

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“…In the future, the proposed ANN-PSOIP algorithm can be used as an accurate/efficient stochastic numerical approach for singular higher order models [58][59][60], biological models [61,62], prediction differential model [63], dynamical investigations of computational fluid models [64][65][66][67][68] and stiff nonlinear systems [69][70][71][72][73][74][75]. Moreover, the polynomial, radial, wavelet, support vector machine-based neural networks looks promising to be exploited in future for the improved performance [76].…”

Section: Discussionmentioning

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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“…Many researchers solved the DD model by considering its significance in various ways; e.g., Bildik et al [21] applied a perturbation iteration scheme, Aziz et al [22] used the Haar wavelet, Tomasiello [23] introduced the fuzzy transform approach, Sabir et al [24] applied heuristic as well as swarm approaches, Erdogan et al [25] presented a finite difference approach, and some other recent related investigations are found in references [26][27][28]. The PD model was recently introduced and its literature form is given as [29]:…”

Section: Introductionmentioning

confidence: 99%

A Neuro-Evolution Heuristic Using Active-Set Techniques to Solve a Novel Nonlinear Singular Prediction Differential Model

et al. 2022

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In this study, a novel design of a second kind of nonlinear Lane–Emden prediction differential singular model (NLE-PDSM) is presented. The numerical solutions of this model were investigated via a neuro-evolution computing intelligent solver using artificial neural networks (ANNs) optimized by global and local search genetic algorithms (GAs) and the active-set method (ASM), i.e., ANN-GAASM. The novel NLE-PDSM was derived from the standard LE and the PDSM along with the details of singular points, prediction terms and shape factors. The modeling strength of ANN was implemented to create a merit function based on the second kind of NLE-PDSM using the mean squared error, and optimization was performed through the GAASM. The corroboration, validation and excellence of the ANN-GAASM for three distinct problems were established through relative studies from exact solutions on the basis of stability, convergence and robustness. Furthermore, explanations through statistical investigations confirmed the worth of the proposed scheme.

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Design of a Novel Second-Order Prediction Differential Model Solved by Using Adams and Explicit Runge–Kutta Numerical Methods

Cited by 20 publications

References 27 publications

A Stochastic Intelligent Computing with Neuro-Evolution Heuristics for Nonlinear SITR System of Novel COVID-19 Dynamics

A Stochastic Intelligent Computing with Neuro-Evolution Heuristics for Nonlinear SITR System of Novel COVID-19 Dynamics

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

A Neuro-Evolution Heuristic Using Active-Set Techniques to Solve a Novel Nonlinear Singular Prediction Differential Model

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