A. Ashyralyev, C. Ashyralyyev, “On the stability of parabolic differential and difference equations with a time-nonlocal condition”, Zh. Vychisl. Mat. Mat. Fiz., 2022, Volume 62, Number 6,Pages <nobr>994

This article is cited in 5 papers

Mathematical physics

On the stability of parabolic differential and difference equations with a time-nonlocal condition

A. Ashyralyev^abc, C. Ashyralyyev^de

^a Department of Mathematics, Bahçesehir University, 34353, Istanbul, Turkey
^b Peoples’ Friendship University of Russia (RUDN University), 117198, Moscow, Russia
^c Institute of Mathematics and Mathematical Modeling, 050010, Almaty, Kazakhstan
^d Department of Engineering Mathematics, Gumushane University, 29100, Gumushane, Turkey
^e Mirzo Ulugbek National University of Uzbekistan, 100174, Tashkent, Uzbekistan

Abstract: In this paper, we study the integral type of the time-nonlocal boundary value problem for a parabolic equation. The well-posedness of these differential and difference problems in Hölder spaces is established. Numerical illustrations in a test case are presented.

Key words: parabolic equation, local and nonlocal problems, difference schemes, stability, Hilbert space.

UDC: 517.9

Received: 24.12.2021
Revised: 24.12.2021
Accepted: 11.02.2022

DOI: 10.31857/S0044466922060023