On graph differential equations and its associated matrix differential equations

J. Vasundhara Devia,*,  R.V.G. Ravi Kumarb and N. Giribabuc

On graph differential equations and its associated matrix differential equations

Authors :

J. Vasundhara Devi^a,*, R.V.G. Ravi Kumar^b and N. Giribabu^c

Author Address :

^a,b,cGVP-Prof.V.Lakshmikantham Institute for Advanced Studies, Department of Mathematics, GVP College of Engineering, Visakhapatnam-530048, Andhra Pradesh, India.

*Corresponding author.

Abstract :

Networks are one of the basic structures in many physical phenomena pertaining to engineering applications. As a network can be represented by a graph which is isomorphic to its adjacency matrix, the study of analysis of networks involving rate of change with respect to time reduces to the study of graph differential equations or equivalently matrix differential equations. In this paper, we develop the basic infrastructure to study the IVP of a graph di.erential equation and the corresponding matrix differential equation. Criteria are obtained to guarantee the existence of a solution and
an iterative technique for convergence to the solution of a matrix di.erential equation is developed.

Keywords :

Dynamic graph, adjacency matrix, graph linear space, graph differential equations, matrix differential equations, existence of a solution, monotone iterative technique.

DOI :

Article Info :

Received : September 12, 2012; Accepted : October 30, 2012.