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 estimates as well as optimal a priori error estimates. Extensive numerical experiments are conducted to verify the promising features of the newly proposed method.

Automated summary

The paper examines numerical solutions for Riesz space fractional partial differential equations with a second order time derivative, proposing a Galerkin finite element scheme and deriving stability and error estimates. Extensive numerical experiments confirm the superior features of the newly proposed method.