Numerical Analysis of Linear and Nonlinear Time-Fractional Subdiffusion Equations

In this paper,a new type of the discrete fractional Gronwall inequality is developed,which is applied to analyze the stability and convergence of a Galerkin spectral method for a linear time-fractional subdifiFusion equation.Based on the temporal-spatial error splitting argument technique,the discrete fractional Gronwall inequality is also applied to prove the unconditional convergence of a semi-implicit Galerkin spectral method for a nonlinear time-fractional subdififusion equation.