On the dynamical behavior of nonlinear Fitzhugh–Nagumo and Bateman–Burger equations in quantum model using Sinc collocation scheme

Ahmad, Iftikhar; Ahmad, Siraj-ul-Islam; Kutlu, Kadir; Ilyas, Hira; Hussain, Syed Ibrar; Rasool, Faiz

doi:10.1140/epjp/s13360-021-02103-6

Cited by 14 publications

(5 citation statements)

References 53 publications

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“…In the future, one may explore the higher-order, singular, and nonlinear kind of partial diferential equations [73][74][75][76][77][78] by using ANNs.…”

Section: Conclusion and Recommendationsmentioning

confidence: 99%

Integrated Stochastic Investigation of Singularly Perturbed Delay Differential Equations for the Neuronal Variability Model

Ahmad,

Hussain,

Ilyas

et al. 2023

International Journal of Intelligent Systems

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The proposed research utilizes a computational approach to attain a numerical solution for the singularly perturbed delay differential equation (SPDDE) problem arising in the neuronal variability model through artificial neural networks (ANNs) with different solvers. The log-sigmoid function is used to construct the fitness function. The implementation of ANN on SPDDE problems is formulated for different solvers and trained with different weights. The optimization solvers such as the genetic algorithm (GA), sequential quadratic programming (SQP), and pattern search (PS) are hybridized with the active set technique (AST) and the interior-point technique (IPT) and is used to check the accuracy and rapid convergence of the numerical results of the SPDDE model. The numerical outcomes demonstrate that the system is easy to handle and efficient to solve with boundary conditions. Moreover, we used the mean residual error for one hundred runs for each solver to validate the accuracy of the proposed scheme.

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“…In the future, one may explore the higher-order, singular, and nonlinear kind of partial diferential equations [73][74][75][76][77][78] by using ANNs.…”

Section: Conclusion and Recommendationsmentioning

confidence: 99%

Integrated Stochastic Investigation of Singularly Perturbed Delay Differential Equations for the Neuronal Variability Model

Ahmad,

Hussain,

Ilyas

et al. 2023

International Journal of Intelligent Systems

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“…Ayub et al [27] scrutinized the heat transfer phenomenon by applying the shooting method on steadystate micropolar fuid. Some useful research related to DEs by numerical techniques is presented by Ahmad et al in [28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Neuro‐Heuristic Computational Intelligence Approach for Optimization of Electro‐Magneto‐Hydrodynamic Influence on a Nano Viscous Fluid Flow

Butt,

Ahmad,

Raja

et al. 2023

International Journal of Intelligent Systems

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In this investigative study, the electro-magneto hydrodynamic (EMHD) influence on a nano viscous fluid model is scrutinized by designing an artificial neural network (ANN) paradigm using a neuro-heuristic approach (NHA) through the combination of GAs (genetic algorithms) and one of the most efficient locally searching solver SQP (sequential quadratic programming), i.e., NHA-GA-SQP. The fluid flow for the proposed problem is initially interpreted in the form of PDEs and then utilization of suitable similarity transformation on these PDEs yields in terms of a stiff nonlinear system of ODEs. The numerical results of the suggested fluidic model based on the variation of its physically existing parameters are calculated through the NHA-GA-SQP solver to detect the variation in velocity, thermal gradient, and concentration during the fluid flow. A detailed analysis of obtained outcomes through the NHA-GA-SQP algorithm and their comparison with the reference results estimated via the Adams method are presented. The calculation of the proposed solver’s accuracy, stability, and consistency through various statistical operators is also involved in the current inspection.

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“…EL‐Aziz studied the numerical solution to investigate the effects of the time‐dependent chemical reactions on the heat and mass transfer of NF and stagnation point flow on the stretching surface 18 . The authors of this research article have done some previous works in the field of differential equations, especially on non‐linear partial differential equations by using a numerical technique to ensure the stability and convergence of the obtained results 19‐22 . Recently, Ahmad et al has worked on a HNF and NF models by using the Lobatto IIIA technique for obtaining the solution of fluidic models 23 …”

Section: Introductionmentioning

confidence: 99%

“…18 The authors of this research article have done some previous works in the field of differential equations, especially on non-linear partial differential equations by using a numerical technique to ensure the stability and convergence of the obtained results. [19][20][21][22] Recently, Ahmad et al has worked on a HNF and NF models by using the Lobatto IIIA technique for obtaining the solution of fluidic models. 23 A few years ago, Noghrehabadi discussed convection through NF over standing plates pasted in permeable medium surface heat flux in Reference 24.…”

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confidence: 99%

A computational convection analysis of SiO₂/water and MoS₂‐SiO₂/water based fluidic system in inverted cone

Hussain

Ahmad

Raja

et al. 2023

Engineering Reports

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A complete shape factor investigation of water‐based mixture type hybrid nanofluid in a permeable boundary with the impact of magnetic field, thick dissemination, and warm radiation is presented in this article. A computational convection analysis of an inverted semi vertical cone with a porous surface in the form of /water nanofluid and /water hybrid nanofluid transport is developed. The system of differential equations is presented and solved numerically by the Lobatto IIIA method. The temperature distributions and fluid velocity are studied along with the coefficient of skin friction and the Nusselt number, taking into account the form of distinct nano‐particles. The flow problem's results are approximated by using several embedding variables. Tables and graphs are constructed for a variety of scenarios including maximum residual error, mesh points, and Nusselt numbers. We conclude that boundary film thickness reduces and the fluid flow is resisted by magnetic field presence. Fluid flow slows down as increases, and this reduction is more evident in nanofluids than in hybrid nanofluids. With an increment in , velocity drops. A detailed analysis of the proposed ordinary differential equations, boundary conditions, and numerical data of skin friction is given both in tabular and graphical forms. Additionally, it is observed that the fluid flow slows down more for the hybrid nanofluid than for the /water nanofluid. Moreover, it is clear that the temperature increase for the /water nanofluid is substantially greater. The authors deduce that the existence of a magnetic field resists fluid flow for hybrid nanofluid forms and decreases the thickness of the viscous boundary layer.

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On the dynamical behavior of nonlinear Fitzhugh–Nagumo and Bateman–Burger equations in quantum model using Sinc collocation scheme

Cited by 14 publications

References 53 publications

Integrated Stochastic Investigation of Singularly Perturbed Delay Differential Equations for the Neuronal Variability Model

Integrated Stochastic Investigation of Singularly Perturbed Delay Differential Equations for the Neuronal Variability Model

Neuro‐Heuristic Computational Intelligence Approach for Optimization of Electro‐Magneto‐Hydrodynamic Influence on a Nano Viscous Fluid Flow

A computational convection analysis of SiO₂/water and MoS₂‐SiO₂/water based fluidic system in inverted cone

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On the dynamical behavior of nonlinear Fitzhugh–Nagumo and Bateman–Burger equations in quantum model using Sinc collocation scheme

Cited by 14 publications

References 53 publications

Integrated Stochastic Investigation of Singularly Perturbed Delay Differential Equations for the Neuronal Variability Model

Integrated Stochastic Investigation of Singularly Perturbed Delay Differential Equations for the Neuronal Variability Model

Neuro‐Heuristic Computational Intelligence Approach for Optimization of Electro‐Magneto‐Hydrodynamic Influence on a Nano Viscous Fluid Flow

A computational convection analysis of SiO2/water and MoS2‐SiO2/water based fluidic system in inverted cone

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A computational convection analysis of SiO₂/water and MoS₂‐SiO₂/water based fluidic system in inverted cone