The Second-Order Accuracy Difference Schemes for Integral-Type Time-Nonlocal Parabolic Problems

This is a discussion on the second order of accuracy difference schemes for approximate solution of the integral type time-nonlocal parabolic problems. Theorems on the stability of r-modified Crank–Nicolson difference schemes and second order of 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 of accuracy in t difference schemes for the one- and multidimensional time-nonlocal parabolic problems are obtained. Numerical results are given.