Local analysis of L1-finite difference method on graded meshes for multi-term two-dimensional time-fractional initial-boundary value problem with Neumann boundary conditions

A multi -term two-dimensional time -fractional initial -boundary value problem, whose boundary conditions are Neumann type, is considered. A temporally graded and spatially uniform mesh is used to apply an L1 -finite difference method. This method involves applying the L1 scheme to discretize each term of the multi -term timefractional derivative and using the finite difference method for spatial discretization. By carefully handling the Neumann boundary discretization, a sharp error analysis is demonstrated at each time level. Numerical results supporting the sharp error estimates of our theoretical results are presented.