Open AccessA Stable Difference Scheme for a Third-Order Partial Differential Equation
Author(s) -
Allaberen Ashyralyev,
Kh. Belakroum
Publication year - 2018
Publication title -
sovremennaâ matematika. fundamentalʹnye napravleniâ
Language(s) - English
Resource type - Journals
eISSN - 2949-0618
pISSN - 2413-3639
DOI - 10.22363/2413-3639-2018-64-1-1-19
Subject(s) - mathematics , hilbert space , boundary value problem , stability (learning theory) , operator (biology) , scheme (mathematics) , mathematical analysis , order (exchange) , boundary (topology) , space (punctuation) , third order , computer science , biochemistry , chemistry , philosophy , theology , finance , repressor , machine learning , transcription factor , economics , gene , operating system
The nonlocal boundary-value problem for a third order partial dierential equation in a Hilbert space H with a self-adjoint positive denite operator A is considered. A stable three-step dierence scheme for the approximate solution of the problem is presented. The main theorem on stability of this dierence scheme is established. In applications, the stability estimates for the solution of dierence schemes of the approximate solution of three nonlocal boundary value problems for third order partial dierential equations are obtained. Numerical results for oneand two-dimensional third order partial dierential equations are provided.