Geodesic
The second-order accuracy difference schemes for integral-type time-nonlocal parabolic problems
Contemporary Mathematics. Fundamental Directions, Contemporary Mathematics. Fundamental Directions, Tome 69 (2023) no. 1, pp. 32-49

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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.
Keywords: nonlocal parabolic problem, second-order accuracy difference scheme, Crank–Nicolson scheme, implicit difference scheme, stability. 
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A. Ashyralyev; Ch. Ashyralyyev. The second-order accuracy difference schemes for integral-type time-nonlocal parabolic problems. Contemporary Mathematics. Fundamental Directions, Contemporary Mathematics. Fundamental Directions, Tome 69 (2023) no. 1, pp. 32-49. http://geodesic.mathdoc.fr/item/CMFD_2023_69_1_a2/