Optimal and near-optimal advection-diffusion finite-difference schemes. II. Unsteadiness and non-uniform grid

2000 ◽  
Vol 456 (1995) ◽  
pp. 489-502 ◽  
Author(s):  
Ronald Smith
Keyword(s):  
Finite Difference ◽  
Difference Schemes ◽  
Uniform Grid ◽  
Finite Difference Schemes ◽  
Advection Diffusion

PARALLEL DOMAIN DECOMPOSITION METHODS WITH THE OVERLAPPING OF SUBDOMAINS FOR PARABOLIC PROBLEMS

1996 ◽  
Vol 06 (08) ◽  
pp. 1169-1185 ◽  
Author(s):  
GRIGORII I. SHISHKIN ◽  
PETR N. VABISHCHEVICH
Keyword(s):  
Finite Difference ◽  
Domain Decomposition ◽  
Domain Decomposition Method ◽  
Approximate Solutions ◽  
Decomposition Methods ◽  
Difference Schemes ◽  
Parabolic Problems ◽  
Uniform Grid ◽  
Finite Difference Schemes ◽  
Dimensional Boundary

For a model of two-dimensional boundary value problem for a second-order parabolic equation, finite difference schemes on the base of a domain decomposition method, oriented on modern parallel computers, is constructed. In the used finite difference schemes iterations at time levels are not applied; some subdomains overlap. We study two classes of schemes characterized by synchronous and asynchronous implementations. It is shown that, under refining grids, the approximate solutions do converge to the exact one in the uniform grid norm.

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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