An α-robust finite difference method for a time-fractional radially symmetric diffusion problem

2021 ◽  
Vol 97 ◽  
pp. 386-393
Author(s):  
Lin Wang ◽  
Martin Stynes
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Diffusion Problem ◽  
Symmetric Diffusion

Convergence in Positive Time for a Finite Difference Method Applied to a Fractional Convection-Diffusion Problem

2018 ◽  
Vol 18 (1) ◽  
pp. 33-42 ◽  
Author(s):  
José Luis Gracia ◽  
Eugene O’Riordan ◽  
Martin Stynes
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Diffusion Problem ◽  
Initial Time ◽  
Uniform Mesh ◽  
Convection Diffusion ◽  
Initial Boundary Value

AbstractA standard finite difference method on a uniform mesh is used to solve a time-fractional convection-diffusion initial-boundary value problem. Such problems typically exhibit a mild singularity at the initial time {t=0}. It is proved that the rate of convergence of the maximum nodal error on any subdomain that is bounded away from {t=0} is higher than the rate obtained when the maximum nodal error is measured over the entire space-time domain. Numerical results are provided to illustrate the theoretical error bounds.

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