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

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Abstract

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.

About the authors

Allaberen Ashyralyev

Bahcesehir University; RUDN University; Institute of Mathematics and Mathematical Modeling

Author for correspondence.
Email: aallaberen@gmail.com
Istanbul, Turkey; Moscow, Russia; Almaty, Kazakhstan

Charyyar Ashyralyyev

Bahcesehir University; National University of Uzbekistan Named After Mirzo Ulugbek

Email: charyar@gmail.com
Istanbul, Turkey; Tashkent, Uzbekistan

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Copyright (c) 2023 Ashyralyev A., Ashyralyyev C.

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