Numerical Methods for the Time Fractional Convection-Diffusion-Reaction Equation

Abstract

In this article, efficient methods are derived for seeking numerical solution to the time fractional convection-diffusion-reaction equation whose solution very likely exhibits a weak regularity at the starting time. Here, the time fractional derivative in the Caputo sense with order in (0, 1) is discretized by the finite difference methods with uniform and non-uniform meshes and the spatial derivative by the local discontinuous Galerkin finite element method. The derived numerical schemes are stable and convergent. Finally, some numerical experiments are presented to verify the theoretical analysis.

Keywords:

• Caputo derivative
• convergence
• local discontinuous Galerkin method
• non-uniform time mesh
• stability

Additional information

Funding

The work was partially supported by the National Natural Science Foundation of China under Grant no. 11671251.