The second-order accuracy difference schemes for integral-type time-nonlocal parabolic problems

This is a discussion on the second-order accuracy difference schemes for approximate solution of the integral-type time-nonlocal parabolic problems. The theorems on the stability of r-modified Crank–Nicolson difference schemes and second-order accuracy implicit difference scheme for approximate solution of the integral-type time-nonlocal parabolic problems in a Hilbert space with self-adjoint positive definite operator are established. In practice, stability estimates for the solutions of the second-order accuracy in $t$ difference schemes for the one and multidimensional time-nonlocal parabolic problems are obtained. Numerical results are given.