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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 valuesdoi:10.14529/jcem180306 fatcat:z7kodeiy3jcqhmqcovm5crvlsi