scholarly journals Numerical Simulation of the Fractal-Fractional Ebola Virus

2020 ◽  
Vol 4 (4) ◽  
pp. 49 ◽  
Author(s):  
H. M. Srivastava ◽  
Khaled M. Saad
Keyword(s):  
Numerical Simulation ◽  
Ebola Virus ◽  
Numerical Solutions ◽  
Finite Difference Methods ◽  
Polynomial Functions ◽  
Fractional Differentiation ◽  
Lagrange Polynomial ◽  
New Models ◽  
Difference Methods ◽  
Two Parameters

In this work we present three new models of the fractal-fractional Ebola virus. We investigate the numerical solutions of the fractal-fractional Ebola virus in the sense of three different kernels based on the power law, the exponential decay and the generalized Mittag-Leffler function by using the concepts of the fractal differentiation and fractional differentiation. These operators have two parameters: The first parameter ρ is considered as the fractal dimension and the second parameter k is the fractional order. We evaluate the numerical solutions of the fractal-fractional Ebola virus for these operators with the theory of fractional calculus and the help of the Lagrange polynomial functions. In the case of ρ=k=1, all of the numerical solutions based on the power kernel, the exponential kernel and the generalized Mittag-Leffler kernel are found to be close to each other and, therefore, one of the kernels is compared with such numerical methods as the finite difference methods. This has led to an excellent agreement. For the effect of fractal-fractional on the behavior, we study the numerical solutions for different values of ρ and k. All calculations in this work are accomplished by using the Mathematica package.

Mimetic seismic wave modeling including topography on deformed staggered grids

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. T125-T141 ◽  
Author(s):  
Josep de la Puente ◽  
Miguel Ferrer ◽  
Mauricio Hanzich ◽  
José E. Castillo ◽  
José M. Cela
Keyword(s):  
Finite Difference ◽  
Seismic Wave ◽  
Seismic Waves ◽  
Numerical Solutions ◽  
Surface Condition ◽  
Finite Difference Methods ◽  
Staggered Grid ◽  
Grid Deformation ◽  
Large Dispersion ◽  
Difference Methods

Finite-difference methods for modeling seismic waves are known to be inaccurate when including a realistic topography, due to the large dispersion errors that appear in the modelled surface waves and the scattering introduced by the staircase approximation to the topography. As a consequence, alternatives to finite-difference methods have been proposed to circumvent these issues. We present a new numerical scheme for 3D elastic wave propagation in the presence of strong topography. This finite-difference scheme is based upon a staggered grid of the Lebedev type, or fully staggered grid (FSG). It uses a grid deformation strategy to make a regular Cartesian grid conform to a topographic surface. In addition, the scheme uses a mimetic approach to accurately solve the free-surface condition and hence allows for a less restrictive grid spacing criterion in the computations. The scheme can use high-order operators for the spatial derivatives and obtain low-dispersion results with as few as six points per minimum wavelength. A series of tests in 2D and 3D scenarios, in which our results are compared to analytical and numerical solutions obtained with other numerical approaches, validate the accuracy of our scheme. The resulting FSG mimetic scheme allows for accurate and efficient seismic wave modelling in the presence of very rough topographies with the advantage of using a structured staggered grid.

scholarly journals Numerical Solutions of the Modified Burgers’ Equation by Finite Difference Methods

2017 ◽  
Vol 13 (1) ◽  
pp. 19-30 ◽  
Author(s):  
Yusuf Ucar ◽  
Nuri Murat Yagmurlu ◽  
Orkun Tasbozan
Keyword(s):  
Stability Analysis ◽  
Finite Difference ◽  
Numerical Solutions ◽  
Burgers Equation ◽  
Finite Difference Methods ◽  
Solution Process ◽  
Modified Burgers Equation ◽  
Finite Difference Equations ◽  
Difference Methods ◽  
Linearization Techniques

Abstract In this study, a numerical solution of the modified Burgers’ equation is obtained by the finite difference methods. For the solution process, two linearization techniques have been applied to get over the non-linear term existing in the equation. Then, some comparisons have been made between the obtained results and those available in the literature. Furthermore, the error norms L2 and L∞ are computed and found to be sufficiently small and compatible with others in the literature. The stability analysis of the linearized finite difference equations obtained by two different linearization techniques has been separately conducted via Fourier stability analysis method.

On the Application of the Collocation Method in Spaces of p-Summable Functions to the Fredholm Integral Equation of the Second Kind

2020 ◽  
pp. 55-60
Author(s):  
Andrei P. Chegolin
Keyword(s):  
Collocation Method ◽  
Numerical Solutions ◽  
Finite Difference Methods ◽  
Pointwise Estimate ◽  
Spline Collocation ◽  
Third Order ◽  
The Third ◽  
Starting Point ◽  
Difference Methods ◽  
Exact Constants

This work is devoted to the study of the numerical solution by the spline collocation method of the Fredholm equation of the second kind. For numerical solutions of such problems, the classical collocation method using polynomials is not always realizable in spaces of p-summable functions for numerical solutions of such problems. It is not always possible to obtain characteristics and estimates of errors of such approximations even in the case of its implementation. In this regard, in recent years, in practice, approximations are built using finite-difference methods. The purpose of this study is to obtain estimates of the error of the obtained approximate solution in the spaces indicated above. In addition, several statements were obtained about a pointwise estimate of this error at collocation nodes in terms of the kernel norm in specially constructed spaces of functions summable over the second variable. To obtain the main results, third-order collocation splines are used, as well as integral and averaged modules of smoothness. In this case, the results obtained can become a starting point for working with collocation splines of higher orders. In the case of the third order, the exact constants involved in the estimates are obtained. These results can be extended to the case of linear, parabolic collocation splines, as well as splines of order higher than the third.

Numerical simulation for solution of SEIR models by meshless and finite difference methods

2020 ◽  
Vol 141 ◽  
pp. 110340 ◽  
Author(s):  
Muhammad Asif ◽  
Zar Ali Khan ◽  
Nadeem Haider ◽  
Qasem Al-Mdallal
Keyword(s):  
Numerical Simulation ◽  
Finite Difference ◽  
Finite Difference Methods ◽  
Difference Methods

Numerical solutions of the nonlinear α-effect dynamo equations

1977 ◽  
Vol 80 (4) ◽  
pp. 769-784 ◽  
Author(s):  
Michael R. E. Proctor
Keyword(s):  
Finite Difference ◽  
Numerical Solutions ◽  
Finite Difference Methods ◽  
Velocity Fields ◽  
Nonlinear Regime ◽  
Small Scale ◽  
Inertial Forces ◽  
Effect Model ◽  
Difference Methods ◽  
Induced Velocity

An extension is made of the α-effect model of the earth's dynamo into the nonlinear regime following the prescription of Malkus & Proctor (1975). In this model, the effects of small-scale dynamics on the α-effect are suppressed, and the global effects of induced velocity fields examined in isolation. The equations are solved numerically using finite-difference methods, and it is shown that viscous and inertial forces are unimportant in the final equilibration, as suggested in the above paper.

Numerical Simulation of Scanning Speed and Supercooling Effects During Zone-Melting-Recrystallization of Soi Wafers

1990 ◽  
Vol 205 ◽  
Author(s):  
Sharon M. Yoon ◽  
Loannis N. Miaoulis
Keyword(s):  
Numerical Simulation ◽  
Finite Difference Methods ◽  
Scanning Speed ◽  
Zone Melting ◽  
Silicon On Insulator ◽  
Total Width ◽  
Temperature Profiles ◽  
Zone Width ◽  
Difference Methods ◽  
Property Changes

AbstractThe effects of scanning speed and supercooling were studied during zone-meltingrecrystallization (ZMR) of silicon-on-insulator (SOI) wafers. Using finite difference methods, a numerical simulation of the ZMR process was developed which captures all of the optical and thermal property changes during phase transformation. The effects of supercooling and scanning speed on the temperature profiles, the total width of the melt-zone and the width of ‘slush’ region were investigated. The melt-zone width increases for increasiongf thdee gfrreeeezsi nogf supercooling and decreases for increasing strip heater velocities. The combined effects on the melt-zone width were shown for various scanning speeds and degrees of supercooling. Supercooling also had a significant effect on the size of the freezing ‘slush’ region which was shown to decrease for increasing degrees of supercooling.

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