ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Nonlocal Boundary Value Problems in Differential and Difference Interpretations for the Generalized Loaded Moisture Transfer Equation


M. KH. Beshtokov

Department of Computational Methods,
Institute of Applied Mathematics and Automation,
Kabardino-Balkarskii Scientific center RAS


We study boundary value problems for a spatially one-dimensional loaded moisture transfer equation of fractional-order with nonlocal boundary conditions. Using the method of energy inequalities, and assuming the existence of a solution of the problem, we derive a priori estimates for the solutions of nonlocal boundary value problems in differential form. Difference schemes are constructed and analogues of a priori estimates in difference form are proved for them; error estimates are given under the assumption of sufficient smoothness of the solutions of the equation. From the obtained a priori estimates, the uniqueness and stability of the solution with respect to the initial data and the right-hand side follow, as well as the convergence of the solution of the difference problem to the solution of the corresponding differential problem at the rate equal to the approximation order of the difference problem.



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