The error analysis of Crank-Nicolson-type difference scheme for fractional subdiffusion equation with spatially variable coefficient

Abstract

A Crank-Nicolson-type difference scheme is presented for the spatial variable coefficient subdiffusion equation with Riemann-Liouville fractional derivative. The truncation errors in temporal and spatial directions are analyzed rigorously. At each time level, it results in a linear system in which the coefficient matrix is tridiagonal and strictly diagonally dominant, so it can be solved by the Thomas algorithm. The unconditional stability and convergence of the scheme are proved in the discrete L2 norm by the energy method. The convergence order is min{2−α2,1+α} in the temporal direction and two in the spatial one. Finally, numerical examples are presented to verify the efficiency of our method.