Sharp analysis of [formula omitted] method on graded mesh for time fractional parabolic differential equation.

In this paper, we study the L 1 − 2 method for solving numerically a class of time fractional parabolic differential equations on a graded mesh. Based on the nonsmooth regularity assumptions, the stability and convergence of the proposed numerical method are investigated. Using rigorous and sharp theoretical analysis, we obtain the optimal graded parameter r = (3 − α) / (1 + α) of the graded mesh. Numerical experiments are given to demonstrate that even if the α is small, the graded mesh based on the optimal graded parameter is still able to recover the optimal convergence order of the L 1 − 2 method. [ABSTRACT FROM AUTHOR]