This article is cited in 26 papers

Differential and difference boundary value problem for loaded third-order pseudo-parabolic differential equations and difference methods for their numerical solution

M. Kh. Beshtokov

Research Institute of Applied Mathematics and Automation, Kabardino-Balkar Research Center, Russian Academy of Sciences, Nalchik, Russia

Abstract: Boundary value problems for loaded third-order pseudo-parabolic equations with variable coefficients are considered. A priori estimates for the solutions of the problems in the differential and difference formulations are obtained. These a priori estimates imply the uniqueness and stability of the solution with respect to the initial data and the right-hand side on a layer, as well as the convergence of the solution of each difference problem to the solution of the corresponding differential problem.

Key words: boundary value problems, a priori estimate, difference scheme, stability and convergence of difference schemes, third-order pseudo-parabolic equation.

UDC: 519.633

Received: 09.11.2015
Revised: 22.10.2016

DOI: 10.7868/S0044466917120092

 English version: Computational Mathematics and Mathematical Physics, 2017, 57:12, 1973–1993

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