On the difference solution of a nonlocal boundary value problem for a fractional diffusion equation

This work investigates a problem for a fractional diffusion equation with nonclassical boundary conditions. A family of weighted difference schemes is studied for the considered problem. An algorithm for finding a numerical solution is provided. Using the maximum principle for the difference problem, an a priori estimate is derived, which implies the stability of the difference schemes and the convergence of the numerical solution to the exact solution in the C-norm.