Analytical and Approximate Solutions of a Novel Nervous Stomach Mathematical Model

Sánchez, Yolanda Guerrero; Sabir, Zulqurnain; Günerhan, Hatıra; Baskonus, Hacı Mehmet

doi:10.1155/2020/5063271

Cited by 59 publications

(23 citation statements)

References 27 publications

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“…A number of numerical formulation schemes have been used by the researcher's community to solve the system of nonlinear equations. Some of them are the differential transformation approach [11], Adams numerical approach [12], variational iteration method [13], Caputo fractional difference scheme [14], and many more [15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Competency of Neural Networks for the Numerical Treatment of Nonlinear Host-Vector-Predator Model

Sabir

Umar

Shah

et al. 2021

Computational and Mathematical Methods in Medicine

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The aim of this work is to introduce a stochastic solver based on the Levenberg-Marquardt backpropagation neural networks (LMBNNs) for the nonlinear host-vector-predator model. The nonlinear host-vector-predator model is dependent upon five classes, susceptible/infected populations of host plant, susceptible/infected vectors population, and population of predator. The numerical performances through the LMBNN solver are observed for three different types of the nonlinear host-vector-predator model using the authentication, testing, sample data, and training. The proportions of these data are chosen as a larger part, i.e., 80% for training and 10% for validation and testing, respectively. The nonlinear host-vector-predator model is numerically treated through the LMBNNs, and comparative investigations have been performed using the reference solutions. The obtained results of the model are presented using the LMBNNs to reduce the mean square error (MSE). For the competence, exactness, consistency, and efficacy of the LMBNNs, the numerical results using the proportional measures through the MSE, error histograms (EHs), and regression/correlation are performed.

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Section: Introductionmentioning

confidence: 99%

Competency of Neural Networks for the Numerical Treatment of Nonlinear Host-Vector-Predator Model

Sabir

Umar

Shah

et al. 2021

Computational and Mathematical Methods in Medicine

Self Cite

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“…In the future, the designed ANN-PSOIPA can be functional to apply to the biological models [58,59] and fluid dynamics models [60][61][62][63].…”

Section: Resultsmentioning

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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“…In future, the LMB designed neural network may be explored for the bioinformatics systems [39][40][41], fractional order systems [42,43], system of nanofluid models [44][45][46][47] and higher order system of equations [48][49][50][51][52]. Additionally, the proposed LMB neural network methodology can be implemented for SIR-based infection spread dynamical models involving high nonlinearity, stiffness, singularities, and delay differentials for the analysis of the models, which still remain challenging traditional/conferential numerical methodologies.…”

Section: Discussionmentioning

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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Analytical and Approximate Solutions of a Novel Nervous Stomach Mathematical Model

Cited by 59 publications

References 27 publications

Competency of Neural Networks for the Numerical Treatment of Nonlinear Host-Vector-Predator Model

Competency of Neural Networks for the Numerical Treatment of Nonlinear Host-Vector-Predator Model

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

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

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