Abstract
This paper analyzes the convergence of the fast L1 method for the semi-linear time-factional subdiffusion equations. The tool we use is the generalized discrete Gronwall inequality. We show that the difference between the solution of the L1 method and the solution of the fast L1 method can be arbitrarily small and is independent of the sizes of the time and/or space grids. Our proof is very simple and is helpful to be used to simplify the convergence analysis of the fast methods for time-fractional evolution equations.
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