Geodesic
A numerical method for solving the second initial-boundary value problem for a multidimensional third-order pseudoparabolic equation
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 31 (2021) no. 3, pp. 384-408

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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.
Mots-clés : pseudoparabolic equation
Keywords: moisture transfer equation, locally one-dimensional scheme, stability, convergence of the difference scheme, additivity of the scheme. 
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     author = {M. Kh. Beshtokov},
     title = {A numerical method for solving the second initial-boundary value problem for a multidimensional third-order pseudoparabolic equation},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {384--408},
     publisher = {mathdoc},
     volume = {31},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2021_31_3_a2/}
}
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M. Kh. Beshtokov. A numerical method for solving the second initial-boundary value problem for a multidimensional third-order pseudoparabolic equation. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 31 (2021) no. 3, pp. 384-408. http://geodesic.mathdoc.fr/item/VUU_2021_31_3_a2/