A predictor–corrector scheme for solving the time fractional Fokker–Planck equation with uniform and non-uniform meshes

In this paper, we combine the predictor–corrector approach with the method of lines and design the predictor–corrector approach with uniform and non-uniform meshes for the numerical solution of the time fractional Fokker–Planck equation in the sense of Caputo derivative. The error bounds of proposed predictor–corrector schemes with uniform and equidistributing meshes are obtained. This work designs efficient numerical schemes, which have linearly increasing computation cost with time but not losing accuracy at the same time, based on the idea of equidistributing meshes. Finally, some results for time-fractional Fokker–Planck equation demonstrate the efficacy and usefulness of the numerical methods.