On a Novel Numerical Scheme for Riesz Fractional Partial Differential Equations

On a Novel Numerical Scheme for Riesz Fractional Partial Differential Equations

In this paper, we consider numerical solutions for Riesz space fractional partial differential equations with a second order time derivative. We propose a Galerkin finite element scheme for both the temporal and spatial discretizations. For the proposed numerical scheme, we derive sharp stability es...

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Bibliographic Details
Main Authors: Junjiang Lai, Hongyu Liu
Format: Article
Language:English
Published: MDPI AG 2021-08-01
Series:Mathematics
Subjects:
Riesz fractional derivative
numerical scheme
bilinear finite element
error estimates
Online Access:https://www.mdpi.com/2227-7390/9/16/2014
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spelling doaj-f19541dd4c12426c8bf2bdb185d0197e2021-08-26T14:02:36ZengMDPI AGMathematics2227-73902021-08-0192014201410.3390/math9162014On a Novel Numerical Scheme for Riesz Fractional Partial Differential EquationsJunjiang Lai0Hongyu Liu1College of Mathematics and Data Science, Minjiang University, Fuzhou 350108, ChinaDepartment of Mathematics, City University of Hong Kong, Hong Kong, ChinaIn this paper, we consider numerical solutions for Riesz space fractional partial differential equations with a second order time derivative. We propose a Galerkin finite element scheme for both the temporal and spatial discretizations. For the proposed numerical scheme, we derive sharp stability estimates as well as optimal a priori error estimates. Extensive numerical experiments are conducted to verify the promising features of the newly proposed method.https://www.mdpi.com/2227-7390/9/16/2014Riesz fractional derivativenumerical schemebilinear finite elementerror estimates
collection DOAJ
language English
format Article
sources DOAJ
author Junjiang Lai
Hongyu Liu
spellingShingle Junjiang Lai
Hongyu Liu
On a Novel Numerical Scheme for Riesz Fractional Partial Differential Equations
Mathematics
Riesz fractional derivative
numerical scheme
bilinear finite element
error estimates
author_facet Junjiang Lai
Hongyu Liu
author_sort Junjiang Lai
title On a Novel Numerical Scheme for Riesz Fractional Partial Differential Equations
title_short On a Novel Numerical Scheme for Riesz Fractional Partial Differential Equations
title_full On a Novel Numerical Scheme for Riesz Fractional Partial Differential Equations
title_fullStr On a Novel Numerical Scheme for Riesz Fractional Partial Differential Equations
title_full_unstemmed On a Novel Numerical Scheme for Riesz Fractional Partial Differential Equations
title_sort on a novel numerical scheme for riesz fractional partial differential equations
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2021-08-01
description In this paper, we consider numerical solutions for Riesz space fractional partial differential equations with a second order time derivative. We propose a Galerkin finite element scheme for both the temporal and spatial discretizations. For the proposed numerical scheme, we derive sharp stability estimates as well as optimal a priori error estimates. Extensive numerical experiments are conducted to verify the promising features of the newly proposed method.
topic Riesz fractional derivative
numerical scheme
bilinear finite element
error estimates
url https://www.mdpi.com/2227-7390/9/16/2014
work_keys_str_mv AT junjianglai onanovelnumericalschemeforrieszfractionalpartialdifferentialequations
AT hongyuliu onanovelnumericalschemeforrieszfractionalpartialdifferentialequations
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