Convergence in Positive Time for a Finite Difference Method Applied to a Fractional Convection-Diffusion Problem-Reference-Cited by-同舟云学术

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

Published:2017-07-06 Issue:1 Volume:18 Page:33-42
ISSN:1609-9389
Container-title:Computational Methods in Applied Mathematics
language:en
Short-container-title:

Author:

Gracia José Luis¹^ORCID,O’Riordan Eugene²,Stynes Martin³^ORCID

Affiliation:

1. Department of Applied Mathematics , University of Zaragoza , 50018 Zaragoza , Spain

2. School of Mathematical Sciences , Dublin City University , Glasnevin , Dublin 9 , Ireland

3. Applied and Computational Mathematics Division , Beijing Computational Science Research Center , Beijing , P. R. China

Abstract

Abstract 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 t = 0

{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

{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.

Funder

National Natural Science Foundation of China

Ministerio de Economía y Competitividad

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis

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