A difference method of solving the Steklov nonlocal boundary value problem of the second kind for the time-fractional diffusion equation

Abstract

We consider difference schemes for the time-fractional diffusion equation with variable coefficients and nonlocal boundary conditions containing real parameters $α$, $β$ and $γ$. By the method of energy inequalities, for the solution of the difference problem, we obtain a priori estimates, which imply the stability and convergence of these difference schemes. The obtained results are supported by the numerical calculations carried out for some test problems.