Numerical investigations to design a novel model based on the fifth order system of Emden–Fowler equations

Sabir, Zulqurnain; Sakar, Mehmet Giyas; Yeskindirova, Manshuk; Saldır, Onur

doi:10.1016/j.taml.2020.01.049

Cited by 55 publications

(22 citation statements)

References 36 publications

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“…So MWNN is the best choice to solve such complicated models using the global and local search terminologies GAIPA. In future, MWNN-GAIPA can be implemented to solve the fluid dynamic nonlinear systems, biological nonlinear systems, singular higher order differential systems, fractional processing, direction of arrival estimation, power and eneggy systems [53][54][55][56][57][58][59][60][61][62].…”

Section: Resultsmentioning

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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Section: Resultsmentioning

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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“…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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“…Nonlinear ordinary differential equations (ODEs) along with associated BCs converted BVP to IVP and then they are integrated by built-in MATLAB tool bvp4c. [61][62][63][64][65][66][67][68][69][70][71] Thus, ruling ODEs are renovated as first-order ODEs. The procedure is given below.…”

Section: Methodsmentioning

confidence: 99%

Higher order chemical process with heat transport of magnetized cross nanofluid over wedge geometry

et al. 2020

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Heat transport keeps vital impact in field of engineering like heat spacing, air conditioning, refrigeration, and in chemical processing, such as heating of base and final products, heat recovery, tempering of containers, autoclaves, and reactors. This manuscript reveals theoretical and an experimental finding related for heat transport of unsteady cross nanofluid and chemical process with inclined magnetic field over the wedge. Heat transport is scrutinized with the existence of nonuniform heat sink source and radiation. Furthermore, mass transfer is studied with higher order chemical process, thermophoresis, and Brownian motion. Mathematical system produces nonlinear partial differential equations (PDEs) of time‐dependent velocity, energy, and concentration. Moreover, these PDEs changed into the system of nonlinear ordinary differential equations (ODEs). The obtained ODEs are passed out through shooting technique to convert the boundary value problem into initial value problem and further bvp4c took them for numerical solution. Bvp4c is MATLAB procedure, which is most convergent for numerical solution of ODEs based on RK‐45 procedure. Many applicable parameters are inspected graphically and in tabular form. Numerical outcomes related to physical quantities are hashed out in tabular form. Chemical process boosts the heat and mass transport. Higher radiation responses higher temperature and inclined magnetic strength reduces the velocity of cross nanofluid.

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Numerical investigations to design a novel model based on the fifth order system of Emden–Fowler equations

Cited by 55 publications

References 36 publications

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

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

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

Higher order chemical process with heat transport of magnetized cross nanofluid over wedge geometry

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