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

Reference10 articles.

1. K. Diethelm, The Analysis of Fractional Differential Equations, Lecture Notes in Math. 2004, Springer, Berlin, 2010.

2. P. A. Farrell, A. F. Hegarty, J. J. H. Miller, E. O’Riordan and G. I. Shishkin, Robust Computational Techniques for Boundary Layers, Appl. Math. Math. Comput. 16, Chapman & Hall/CRC, Boca Raton, 2000.

3. J. L. Gracia, E. O’Riordan and M. Stynes, Convergence outside the initial layer for a numerical method for the time-fractional heat equation, Numerical Analysis and Its Applications, Lecture Notes in Comput. Sci. 10187, Springer, Cham (2017), 82–94.

4. B. Jin, R. Lazarov and Z. Zhou, An analysis of the L1 scheme for the subdiffusion equation with nonsmooth data, IMA J. Numer. Anal. 36 (2016), no. 1, 197–221.

5. B. Jin and Z. Zhou, An analysis of Galerkin proper orthogonal decomposition for subdiffusion, ESAIM Math. Model. Numer. Anal. 51 (2017), no. 1, 89–113.

Cited by 43 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Temporal second-order fully discrete two-grid methods for nonlinear time-fractional variable coefficient diffusion-wave equations;Applied Mathematics and Computation;2024-04

2. Local analysis of L1-finite difference method on graded meshes for multi-term two-dimensional time-fractional initial-boundary value problem with Neumann boundary conditions;Computers & Mathematics with Applications;2024-03

3. A robust higher-order finite difference technique for a time-fractional singularly perturbed problem;Mathematics and Computers in Simulation;2024-01

4. A fast compact difference scheme with unequal time-steps for the tempered time-fractional Black–Scholes model;International Journal of Computer Mathematics;2023-09-06

5. Analytical and Numerical Solution for the Time Fractional Black-Scholes Model Under Jump-Diffusion;Computational Economics;2023-04-19