Author(s)

Y.A. Melnikov & T.M. Hall

Abstract

The first attempt is made to extend the Green's (influence) function formal- ism to boundary value problems stated for a special type of linear systems of ordinary differential equations which are formulated on finite weighted graphs. Every equation in such a system governs a single unknown function and is stated on a single edge of the graph. The separate equations are put into a system format by providing the contact conditions at each of the vertices of the graph of degree greater than or equal to two, while the boundary conditions are formulated at each of the endpoints of the graph. Some applications are discussed in one-dimensional and two-dimensional steady-state heat conduction and in Kirchhoff's beam theory. 1 Introduction The significance of the Green's functions f

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