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 J. Comp. Eng. Math., 2018, Volume 5, Issue 3, Pages 61–74 (Mi jcem127)

Computational Mathematics

Numerical solution for non-stationary linearized Hoff equation defined on geometrical graph

M. A. Sagadeeva, A. V. Generalov

South Ural State University, Chelyabinsk, Russian Federation

Abstract: The non-stationary linearized Hoff equation is considered in the article. For this equation, a solution is obtained both on the domain and on the geometric graph. For the five-edged graph, the Sturm – Liouville problem is solved to obtain a numerical solution of the non-stationary linearized Hoff equation on the graph. A numerical method for solving this equation on a graph is described. The graphics for obtained numerical solution are constructed at different instants of time for given values of the equation parameters and functions. The article besides the introduction and the bibliography contains four parts. The first part contains information on abstract non-stationary Sobolev type equations, and solutions for the non-stationary linearized Hoff equation on the domain are constructed. In the second one we consider the Sturm – Liouville problem on a graph and construct necessary spaces and operators on graphs. In the third one we study the solvability of the non-stationary linearized Hoff equation on the five-edged graph, and finally, in the last part we describe the numerical solution of the equation on the graph and the graphics of these solutions at different instants of time.

Keywords: Sobolev type equation, relatively bounded operator, Sturm – Liouville problem, Laplace operator on graph.

DOI: https://doi.org/10.14529/jcem180306

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Bibliographic databases:

UDC: 517.9
MSC: 35G05
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Citation: M. A. Sagadeeva, A. V. Generalov, “Numerical solution for non-stationary linearized Hoff equation defined on geometrical graph”, J. Comp. Eng. Math., 5:3 (2018), 61–74

Citation in format AMSBIB
\Bibitem{SagGen18} \by M.~A.~Sagadeeva, A.~V.~Generalov \paper Numerical solution for non-stationary linearized Hoff equation defined on geometrical graph \jour J. Comp. Eng. Math. \yr 2018 \vol 5 \issue 3 \pages 61--74 \mathnet{http://mi.mathnet.ru/jcem127} \crossref{https://doi.org/10.14529/jcem180306} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3858979} \elib{http://elibrary.ru/item.asp?id=35669830}