scholarly journals Finite Difference Method for Two-Sided Two Dimensional Space Fractional Convection-Diffusion Problem with Source Term

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1878
Author(s):  
Eyaya Fekadie Anley ◽  
Zhoushun Zheng
Keyword(s):  
Diffusion Equation ◽  
Source Term ◽  
Diffusion Problem ◽  
Stability And Convergence ◽  
Difference Approximation ◽  
Finite Domain ◽  
Two Dimensional ◽  
Convection Diffusion ◽  
Nicolson Scheme ◽  
Crank Nicolson

In this paper, we have considered a numerical difference approximation for solving two-dimensional Riesz space fractional convection-diffusion problem with source term over a finite domain. The convection and diffusion equation can depend on both spatial and temporal variables. Crank-Nicolson scheme for time combined with weighted and shifted Grünwald-Letnikov difference operator for space are implemented to get second order convergence both in space and time. Unconditional stability and convergence order analysis of the scheme are explained theoretically and experimentally. The numerical tests are indicated that the Crank-Nicolson scheme with weighted shifted Grünwald-Letnikov approximations are effective numerical methods for two dimensional two-sided space fractional convection-diffusion equation.

scholarly journals The difference scheme for the two-dimensional convection-diffusion problem for large peclet numbers

2018 ◽  
Vol 226 ◽  
pp. 04030 ◽  
Author(s):  
Alexander I. Sukhinov ◽  
Alexander E. Chistyakov ◽  
Yulia V. Belova
Keyword(s):  
Diffusion Equation ◽  
Difference Scheme ◽  
Diffusion Problem ◽  
Two Dimensional ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
The Difference

The purpose of this work is the development of a difference scheme for the solution of convection-diffusion problem at high Peclet numbers (Pe>2). In accordance with this purpose the following problems were solved: difference scheme for convection is built, comparison with the existing schemes is carried out; conditions for stability of the proposed difference scheme are obtained. Solutions of the convection-diffusion equation on the basis of the proposed difference scheme at various Peclet numbers are obtained.

The Best Perturbation Method for the Parameter Inversion of Two-Dimension Convection-Diffusion Equation

2013 ◽  
Vol 380-384 ◽  
pp. 1143-1146
Author(s):  
Xiang Guo Liu
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Perturbation Method ◽  
Numerical Simulations ◽  
Numerical Solution ◽  
Two Dimensional ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Parameter Inversion ◽  
Parametric Inversion

The paper researches the parametric inversion of the two-dimensional convection-diffusion equation by means of best perturbation method, draw a Numerical Solution for such inverse problem. It is shown by numerical simulations that the method is feasible and effective.

scholarly journals Crank-Nicolson scheme for two-dimensional in space fractional diffusion equations with functional delay

2021 ◽  
Vol 57 ◽  
pp. 128-141
Author(s):  
M. Ibrahim ◽  
V.G. Pimenov
Keyword(s):  
Piecewise Linear ◽  
Linear Interpolation ◽  
Fractional Diffusion ◽  
Dimensional System ◽  
Two Dimensional ◽  
Piecewise Linear Interpolation ◽  
Functional Delay ◽  
General Difference ◽  
Nicolson Scheme ◽  
Crank Nicolson

A two-dimensional in space fractional diffusion equation with functional delay of a general form is considered. For this problem, the Crank-Nicolson method is constructed, based on shifted Grunwald-Letnikov formulas for approximating fractional derivatives with respect to each spatial variable and using piecewise linear interpolation of discrete history with continuation extrapolation to take into account the delay effect. The Douglas scheme is used to reduce the emerging high-dimensional system to tridiagonal systems. The residual of the method is investigated. To obtain the order of the method, we reduce the systems to constructions of the general difference scheme with heredity. A theorem on the second order of convergence of the method in time and space steps is proved. The results of numerical experiments are presented.

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