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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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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1721191764691255296 |