A study of the stability for a generalized finite-difference scheme applied to the advection–diffusion equation

2020 ◽  
Vol 176 ◽  
pp. 301-311 ◽  
Author(s):  
G. Tinoco-Guerrero ◽  
F.J. Domínguez-Mota ◽  
J.G. Tinoco-Ruiz
Keyword(s):  
Finite Difference ◽  
Diffusion Equation ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
The Stability

scholarly journals Computationally Efficient Hybrid Method for the Numerical Solution of the 2D Time Fractional Advection-Diffusion Equation

2020 ◽  
Vol 5 (3) ◽  
pp. 432-446
Author(s):  
Fouad Mohammad Salama ◽  
Norhashidah Hj. Mohd Ali
Keyword(s):  
Finite Difference ◽  
Diffusion Equation ◽  
Difference Scheme ◽  
Numerical Solution ◽  
Hybrid Method ◽  
Finite Difference Scheme ◽  
Computational Cost ◽  
Stability And Convergence ◽  
Advection Diffusion Equation ◽  
Advection Diffusion

In this paper, a hybrid method based on the Laplace transform and implicit finite difference scheme is applied to obtain the numerical solution of the two-dimensional time fractional advection-diffusion equation (2D-TFADE). Some of the major limitations in computing the numerical solution for fractional differential equations (FDEs) in multi-dimensional space are the huge computational cost and storage requirement, which are O(N^2) cost and O(MN) storage, N and M are the total number of time levels and space grid points, respectively. The proposed method reduced the computational complexity efficiently as it requires only O(N) computational cost and O(M) storage with reasonable accuracy when numerically solving the TFADE. The method’s stability and convergence are also investigated. The Results of numerical experiments of the proposed method are obtained and found to compare well with the results of existing standard finite difference scheme.

scholarly journals Stability analysis of finite difference schemes for an advection diffusion equation

2017 ◽  
Vol 29 (2) ◽  
pp. 143-151 ◽  
Author(s):  
TMAK Azad ◽  
LS Andallah
Keyword(s):  
Stability Analysis ◽  
Finite Difference ◽  
Diffusion Equation ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Time Step ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
The Stability ◽  
Stability Results

The paper studies stability analysis for two standard finite difference schemes FTBSCS (forward time backward space and centered space) and FTCS (forward time and centered space). One-dimensional advection diffusion equation is solved by using the schemes with appropriate initial and boundary conditions. Numerical experiments are performed to verify the stability results obtained in this study. It is found that FTCS scheme gives better point-wise solutions than FTBSCS in terms of time step selection.Bangladesh J. Sci. Res. 29(2): 143-151, December-2016

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