A numerical method for solving the second initial-boundary value problem for a multidimensional third-order pseudoparabolic equation | Zendy

M. Kh. Beshtokov | Zendy

Open Access

A numerical method for solving the second initial-boundary value problem for a multidimensional third-order pseudoparabolic equation

Author(s) -

M. Kh. Beshtokov

Publication year - 2021

Publication title -

vestnik udmurtskogo universiteta matematika mekhanika komp yuternye 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.

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