Geodesic
Summary approximation method for a third order multidimensional pseudoparabolic equation
Matematičeskaâ fizika i kompʹûternoe modelirovanie, Tome 24 (2021) no. 4, pp. 5-18.

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In this paper we study the first initial-boundary value problem for a multidimensional pseudoparabolic equation of the third order. Assuming the existence of a regular solution to the problem posed, an a priori estimate is obtained in differential form, which implies the uniqueness and stability of the solution with respect to the right-hand side and initial data. A locally one-dimensional difference scheme is constructed and an a priori estimate in the difference form is obtained for its solution. The stability and convergence of the locally one-dimensional difference scheme are proved. Numerical calculations are performed using test examples to illustrate the theoretical calculations obtained in this work.
Keywords: boundary value problems, modified moisture transfer equation, locally one-dimensional scheme, stability and convergence of the scheme, schema additivity.
Mots-clés : a priori estimation, pseudoparabolic equation 
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     author = {M. KH. Beshtokov and V. A. Vogahova and M. H. Shhanukov-Lafishev},
     title = {Summary approximation method for a third order multidimensional pseudoparabolic equation},
     journal = {Matemati\v{c}eska\^a fizika i kompʹ\^uternoe modelirovanie},
     pages = {5--18},
     publisher = {mathdoc},
     volume = {24},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VVGUM_2021_24_4_a0/}
}
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M. KH. Beshtokov; V. A. Vogahova; M. H. Shhanukov-Lafishev. Summary approximation method for a third order multidimensional pseudoparabolic equation. Matematičeskaâ fizika i kompʹûternoe modelirovanie, Tome 24 (2021) no. 4, pp. 5-18. http://geodesic.mathdoc.fr/item/VVGUM_2021_24_4_a0/