On a Novel Numerical Scheme for Riesz Fractional Partial Differential Equations

Junjiang Lai and Hongyu Liu
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Junjiang Lai: College of Mathematics and Data Science, Minjiang University, Fuzhou 350108, China
Hongyu Liu: Department of Mathematics, City University of Hong Kong, Hong Kong, China

Mathematics, 2021, vol. 9, issue 16, 1-14

Abstract: 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.

Keywords: Riesz fractional derivative; numerical scheme; bilinear finite element; error estimates (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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