Open AccessA numerical method for solving the second initial-boundary value problem for a multidimensional third-order pseudoparabolic equation
Author(s) -
М. Х. Бештоков
Publication year - 2021
Publication title -
vestnik udmurtskogo universiteta. matematika, mehanika, kompʹûternye nauki
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.354
H-Index - 8
eISSN - 2076-5959
pISSN - 1994-9197
DOI - 10.35634/vm210303
Subject(s) - mathematics , boundary value problem , mathematical analysis , differential equation , a priori and a posteriori , norm (philosophy) , partial differential equation , convergence (economics) , initial value problem , stability (learning theory) , a priori estimate , variable (mathematics) , philosophy , epistemology , machine learning , political science , computer science , law , economics , economic growth
The work is devoted to the study of the second initial-boundary value problem for a general-form third-order differential equation of pseudoparabolic type with variable coefficients in a multidimensional domain with an arbitrary boundary. In this paper, a multidimensional pseudoparabolic equation is reduced to an integro-differential equation with a small parameter, and a locally one-dimensional difference scheme by A.A. Samarskii is used. Using the maximum principle, an a priori estimate is obtained for the solution of a locally one-dimensional difference scheme in the uniform metric in the $C$ norm. The stability and convergence of the locally one-dimensional difference scheme are proved.