This article is cited in 3 papers

Mathematical Modelling, Numerical Methods and Software Systems

To nonlocal boundary value problems for a multidimensional parabolic equation with variable coefficients

Z. V. Beshtokova

Institute of Applied Mathematics and Automation, Nalchik

Abstract: The paper studies nonlocal boundary value problems for a parabolic equation with variable coefficients in a multidimensional domain. Studies of the set nonlocal boundary value problems are carried out assuming the existence of a regular solution. To solve the corresponding differential problem under consideration by the method of energy inequalities, a priori estimates in the differential and difference interpretations are obtained. From the obtained a priori estimates the uniqueness and stability of the solution on the right side and the initial data, as well as the convergence of the solution of the difference problem to the solution of the corresponding differential problem at a rate of $O(|h|+\tau)$, follow.

Keywords: a priori estimation, parabolic equation, multidimensional equation, difference scheme, stability and convergence of difference schemes, nonlocal condition.

Received: 29.01.2019
Revised: 26.05.2019

DOI: 10.26456/vtpmk535

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