scholarly journals Qualitative properties of one-dimensional fractional differential advection-diffusion equation

Vestnik MGSU ◽  
2014 ◽  
pp. 28-33
Author(s):  
L. M. Isaeva ◽  
T. S. Aleroev
Keyword(s):  
Diffusion Equation ◽  
Qualitative Properties ◽  
One Dimensional ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Fractional Differential ◽  
Differential Advection

scholarly journals Time-Splitting Procedures for the Numerical Solution of the 2D Advection-Diffusion Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-20 ◽  
Author(s):  
A. R. Appadu ◽  
H. H. Gidey
Keyword(s):  
Diffusion Equation ◽  
Numerical Solution ◽  
Optimization Technique ◽  
Step Size ◽  
One Dimensional ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Optimal Value ◽  
Time Splitting ◽  
Dispersion And Dissipation Errors

We perform a spectral analysis of the dispersive and dissipative properties of two time-splitting procedures, namely, locally one-dimensional (LOD) Lax-Wendroff and LOD (1, 5) [9] for the numerical solution of the 2D advection-diffusion equation. We solve a 2D numerical experiment described by an advection-diffusion partial differential equation with specified initial and boundary conditions for which the exact solution is known. Some errors are computed, namely, the error rate with respect to theL1norm, dispersion and dissipation errors. Lastly, an optimization technique is implemented to find the optimal value of temporal step size that minimizes the dispersion error for both schemes when the spatial step is chosen as 0.025, and this is validated by numerical experiments.

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