A Legendre spectral method on graded meshes for the two-dimensional multi-term time-fractional diffusion equation with non-smooth solutions

Abstract

In this paper, we consider a Legendre spectral method on graded meshes for solving the two-dimensional multi-term time-fractional diffusion equation with non-smooth solutions. The L1 method on graded meshes is developed in temporal direction. In the spatial direction, we choose the Legendre spectral method. With the help of mathematical induction method, the stability and convergence of the above mentioned method are theoretically proved. To improve the computational efficiency, we use the fast algorithm in the numerical implementation. Some numerical results are provided to verify the theoretical analysis and demonstrate the effectiveness of our method.