Local Error Estimate of an L1-Finite Difference Scheme for the Multiterm Two-Dimensional Time-Fractional Reaction-Diffusion Equation with Robin Boundary Conditions

In this paper, the numerical method for a multiterm time-fractional reaction-diffusion equation with classical Robin boundary conditions is considered. The full discrete scheme is constructed with the L1-finite difference method, which entails using the L1 scheme on graded meshes for the temporal discretisation of each Caputo fractional derivative and using the finite difference method on uniform meshes for spatial discretisation. By dealing with the discretisation of Robin boundary conditions carefully, sharp error analysis at each time level is proven. Additionally, numerical results that can confirm the sharpness of the error estimates are presented.