Numerical methods for time-fractional subdiffusion equations: Convolution quadrature with block generalized Adams methods

This paper studies a class of time-fractional subdiffusion equations. The temporal approximation is achieved using convolution quadrature, developed via the block generalized Adams method. By incorporating a correction term, we derive the convergence bound for the semi-discrete scheme in time. Additionally, the stability of the convolution quadrature is analyzed. Furthermore, the spectral collocation method is employed for spatial approximation. Both theoretical and numerical evidences demonstrate that the proposed scheme achieves high-order convergence even with a uniform grid for temporal discretization.