Efficient L1-ADI finite difference method for the two-dimensional nonlinear time-fractional diffusion equation

In this work, we propose an efficient finite difference method for the two-dimensional nonlinear time -fractional diffusion equation with weakly singular solutions. By using backward formula for the approximation of nonlinear term, and L1 scheme on uniform mesh for discretisation of temporal Caputo fractional derivative, a linear scheme is constructed and analysed. Stability and pointwise-in-time convergence of the fully discrete scheme are rigorously established. Numerical results are provided to confirm the sharpness of theoretical analysis.