Abstract:
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.
Key words:Caputo fractional derivative, fractional diffusion equation, boundary value problem, maximum principle, a priori estimate, approximation, stability of difference schemes, convergence of difference schemes, nonlocal boundary value problem.
