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Bazzaev, Alexander K.; Gutnova, Dzerassa K.

About convergence of difference schemes for a third-order pseudo-parabolic equation with nonlocal boundary value condition. (English) Zbl 1473.65266

Sib. Èlektron. Mat. Izv. 18, No. 1, 548-560 (2021).
Summary: A nonlocal boundary value problem for a third-order pseudoparabolic 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.

MSC:

65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N06 Finite difference methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs

Keywords:

boundary value problem; nonlocal boundary value problem; nonlocal condition; third-order pseudo-parabolic equation; difference schemes; stability and convergence of difference schemes; a priori estimates; energy inequality method
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\textit{A. K. Bazzaev} and \textit{D. K. Gutnova}, Sib. Èlektron. Mat. Izv. 18, No. 1, 548--560 (2021; Zbl 1473.65266)
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