
Computational Mathematics
Numerical solution for nonstationary linearized Hoff equation defined on geometrical graph
M. A. Sagadeeva^{}, A. V. Generalov^{} ^{} South Ural State University, Chelyabinsk, Russian Federation
Abstract:
The nonstationary 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 fiveedged graph, the Sturm – Liouville problem is solved to obtain a numerical solution of the nonstationary 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 nonstationary Sobolev type equations, and solutions for the nonstationary 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 nonstationary linearized Hoff equation on the fiveedged 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 Received: 07.07.2018
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Citation:
M. A. Sagadeeva, A. V. Generalov, “Numerical solution for nonstationary 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 nonstationary linearized Hoff equation defined on geometrical graph
\jour J. Comp. Eng. Math.
\yr 2018
\vol 5
\issue 3
\pages 6174
\mathnet{http://mi.mathnet.ru/jcem127}
\crossref{https://doi.org/10.14529/jcem180306}
\mathscinet{http://www.ams.org/mathscinetgetitem?mr=3858979}
\elib{http://elibrary.ru/item.asp?id=35669830}
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