Numerical method for space degenerate fractional derivative problems of atmospheric pollution.

In this work we consider time fractional advection-diffusion problems of air pollution with vertical diffusion coefficient. The mathematical model is a degenerate parabolic equation with point sources. Discontinuity of the diffusion coefficient may also appear. We construct efficient second-order numerical scheme for solving the problem. The fractional derivative in the Caputo sense is approximated by L1 formula. For the resulting semidiscrete problem we develop exponential numerical scheme. Numerical experiments, performed on appropriate graded spatial and temporal meshes, illustrate the efficiency of the proposed method for degenerate and discontinuous diffusivity. [ABSTRACT FROM AUTHOR]