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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Published in:	Journal of computational methods in applied mathematics Vol. 18; no. 1; pp. 33 - 42
Main Authors:	Gracia, José Luis, O’Riordan, Eugene, Stynes, Martin
Format:	Journal Article
Language:	English
Published:	Minsk De Gruyter 01.01.2018 Walter de Gruyter GmbH
Subjects:	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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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 . 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.
AbstractList	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. 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. 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 [Image omitted]. It is proved that the rate of convergence of the maximum nodal error on any subdomain that is bounded away from [Image omitted] 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.
Author	Gracia, José Luis Stynes, Martin O’Riordan, Eugene
Author_xml	– sequence: 1 givenname: José Luis orcidid: 0000-0003-2538-9027 surname: Gracia fullname: Gracia, José Luis email: jlgracia@unizar.es organization: Department of Applied Mathematics, University of Zaragoza, 0018Zaragoza, Spain – sequence: 2 givenname: Eugene surname: O’Riordan fullname: O’Riordan, Eugene email: eugene.oriordan@dcu.ie organization: School of Mathematical Sciences, Dublin City University, Glasnevin, Dublin9, Ireland – sequence: 3 givenname: Martin orcidid: 0000-0003-2085-7354 surname: Stynes fullname: Stynes, Martin email: m.stynes@csrc.ac.cn organization: Applied and Computational Mathematics Division, Beijing Computational Science Research Center, Beijing, P. R. China
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Snippet	A standard finite difference method on a uniform mesh is used to solve a time-fractional convection-diffusion initial-boundary value problem. Such problems...
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SubjectTerms	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
Title	Convergence in Positive Time for a Finite Difference Method Applied to a Fractional Convection-Diffusion Problem
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