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

A 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 . It is proved that the rate of convergence of the maximum nodal error on any subdomain...

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Veröffentlicht in:Journal of computational methods in applied mathematics Jg. 18; H. 1; S. 33 - 42
Hauptverfasser: Gracia, José Luis, O’Riordan, Eugene, Stynes, Martin
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Minsk De Gruyter 01.01.2018
Walter de Gruyter GmbH
Schlagworte:
65M06
65M12
65M15
Boundary value problems
Caputo Fractional Derivative
Convection-diffusion equation
Convergence
Error analysis
Finite difference method
Initial Boundary Value Problem
L1 Scheme
Mathematical analysis
Weak Singularity
ISSN:1609-4840, 1609-9389
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Beschreibung
Zusammenfassung:A 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 . It is proved that the rate of convergence of the maximum nodal error on any subdomain that is bounded away from 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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ISSN:1609-4840
1609-9389
DOI:10.1515/cmam-2017-0019