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...
Main Authors: | , |
---|---|
Format: | Article |
Language: | English |
Published: |
MDPI AG
2021-08-01
|
Series: | Mathematics |
Subjects: | |
Online Access: | https://www.mdpi.com/2227-7390/9/16/2014 |
Summary: | 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. |
---|---|
ISSN: | 2227-7390 |