Modeling and Numerical Simulation for Covering the Fractional COVID-19 Model Using Spectral Collocation-Optimization Algorithm

Khader, M. M.; Adel, Mohamed

doi:10.3390/fractalfract6070363

Cited by 12 publications

(3 citation statements)

References 36 publications

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“…There are many techniques that were used to solve fractional differential equations (FDEs) [7][8][9][10]; for example, the FEM was applied in many papers for solving FDEs and the results were excellent [11][12][13][14][15]. The studied model ( 2)-( 4) was considered by many mathematicians due to its wide range of applications, and many techniques were applied to simulate it like the finite difference methods (FDM) and their extensions [16][17][18].…”

Section: Basic Concepts On the Proposed Modelmentioning

confidence: 99%

An efficient class of discrete finite difference/element scheme for solving the fractional reaction subdiffusion equation

Khader

2023

Math Methods in App Sciences

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An estimate for the fractional reaction subdiffusion equation is presented by a discrete Crank-Nicolson finite element method (FEM), which we can obtain by using the finite difference method (FDM) (in time) and the finite element method (in space). The proposed scheme is obtained at time t n+ 1 2 because at this time there are some different coefficients compared to those at time t n+1 , that is,. We studied the stability analysis, truncation error, and convergence analysis of the derived scheme. Numerical examples are presented to illustrate the efficiency of the given algorithm.

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Section: Basic Concepts On the Proposed Modelmentioning

confidence: 99%

An efficient class of discrete finite difference/element scheme for solving the fractional reaction subdiffusion equation

Khader

2023

Math Methods in App Sciences

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“…Many academics have successfully used a variety of numerical and approximation approaches to solve ODEs. When dealing with this kind of issue, the finite element approach (FEM) [14] has a number of benefits because the coefficients for the solution can be quickly acquired using any of the available numerical programs. In the paragraphs that follow, we'll go through this method's primary benefits:…”

Section: Introductionmentioning

confidence: 99%

Studying of the Covid-19 model by using the finite element method: theoretical and numerical simulation

Alhejili,

Khader,

Lotfy

et al. 2023

Soft Comput

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This study simulates the start of coronavirus infection using a mathematical model based on ordinary differential equations . Additionally, provide the numerical treatment and simulation of this model using the finite element approach (FEM). The goal of this research is to stop and slow the spread of a sickness that is ravaging the globe. A susceptible person may also transfer immediately to the quarantined class after the exposed person has been quarantined or moved to one of the contaminated classes. This model was employed by the researchers to account for both asymptomatic and symptomatic infected people. The proposed model is reduced to a set of algebraic equations using the FEM. The resulting system is then created as an optimization problem with constraints, which is subsequently optimized to obtain the solution and the unknown coefficients. The obtained findings are compared to those produced using the fourth-order Runge-Kutta method (RK4). Finally, we calculate the residual error function of the approximation in order to validate the FEM, and it is presented in symmetric forms.

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“…The proof of the three items in this theorem can be found in [35,36]. The given data here are utilized to estimate parameters using the least curve fitting method.…”

mentioning

confidence: 99%

Numerical Simulation for COVID-19 Model Using a Multidomain Spectral Relaxation Technique

et al. 2023

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The major objective of this work is to evaluate and study the model of coronavirus illness by providing an efficient numerical solution for this important model. The model under investigation is composed of five differential equations. In this study, the multidomain spectral relaxation method (MSRM) is used to numerically solve the suggested model. The proposed approach is based on the hypothesis that the domain of the problem can be split into a finite number of subintervals, each of which can have a solution. The procedure also converts the proposed model into a system of algebraic equations. Some theoretical studies are provided to discuss the convergence analysis of the suggested scheme and deduce an upper bound of the error. A numerical simulation is used to evaluate the approach’s accuracy and utility, and it is presented in symmetric forms.

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Modeling and Numerical Simulation for Covering the Fractional COVID-19 Model Using Spectral Collocation-Optimization Algorithm

Cited by 12 publications

References 36 publications

An efficient class of discrete finite difference/element scheme for solving the fractional reaction subdiffusion equation

An efficient class of discrete finite difference/element scheme for solving the fractional reaction subdiffusion equation

Studying of the Covid-19 model by using the finite element method: theoretical and numerical simulation

Numerical Simulation for COVID-19 Model Using a Multidomain Spectral Relaxation Technique

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