TRANSFORMATION OF A BOUNDARY VALUE PROBLEM ON A GRAPH INTO A BOUNDARY VALUE PROBLEM FOR A SYSTEM

Differential equations found in different applications, can be interpreted as equations in graphs. There is good reason to argue that the theory of such equations can be applied on a large scale, and on the other hand, the properties of the graph can be used to create a qualitative theory of such equations and methods for solving them. The first graph model was used in chemistry. The development of the theory of differential operators in graphs has occurred recently, most of the research in this area has been carried out in the last two decades.
Differential operators in graphs appeared in chemistry, physics and engineering (nanotechnology) and are of mathematical interest. Applications of differential operators in graphs include the theory of free electrons of conjugated molecules in chemistry, quantum wires and quantum chaos, scattering theory, and photonic crystals.
Many function spaces are defined on graphs. Using these spaces of functions and differential systems, we define boundary value problems in graphs. In this article, we consider the transformation of a boundary value problem on a graph into a boundary value problem for a differential system. To do this, we have transformed each edge of the graph into the interval (0, 1) and redefined the differential equation on the graph. Then we changed the boundary conditions in accordance with the interval and established a connection between the original boundary value problem and the newly obtained boundary value problem.

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