A Higher Order Difference Scheme for the Time Fractional Diffusion Equation with the Steklov Nonlocal Boundary Value Problem of the Second Kind
We consider finite-difference schemes of higher order approximation for the time fractional diffusion equation with nonlocal boundary conditions containing real parameters \(\alpha \), \(\beta \) and \(\gamma \). We obtain a priori estimates for the solution of the difference problem, which imply the stability and convergence of the constructed difference schemes. The obtained results are supported by the numerical calculations carried out for some test problems as well.
This work is executed under grant of the President of the Russian Federation for the state support of young Russian scientists MK–3360.2015.1.