Differentical equations, dynamical systems and optimal control

About convergence of difference schemes for a third-order pseudo-parabolic equation with nonlocal boundary value condition

A. K. Bazzaev^ab, D. K. Gutnova<sup>b

a</sup> North Ossetian State University after K.L. Khetagurov, 44-46, Vatutina str., Vladikavkaz, 362025, North Ossetia – Alania, Russia
^b Vladikavkaz Institute of Management, 14, Borodinskaya str., Vladikavkaz, 362025, North Ossetia – Alania, Russia

Abstract: A nonlocal boundary value problem for a third-order pseudo-parabolic equation with variable coefficients is considered. For solving this problem, a priori estimates in the differential and difference forms are obtained. The obtained a priori estimates imply the uniqueness and stability of the solution on a layer with respect to the initial data and the right-hand side and the convergence of the solution of the difference problem to the solution of the differential problem.

Keywords: boundary value problem, a nonlocal boundary value problem, a nonlocal condition, a third-order pseudo-parabolic equation, difference schemes, stability and convergence of difference schemes, a priori estimates, energy inequality method.

UDC: 519.633

MSC: 65M12

Received July 13, 2020, published May 25, 2021

Language: English

DOI: 10.33048/semi.2021.18.040

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