Existence results for Graph Differential Equations through its Associated Matrix Differential Equations

R.V.G.RaviKumar,hodmaths@gvpce.ac.in S.Srinivasa Rao

Abstract


A network can be represented by graph which is isomorphic to its adjacency matrix. Thus the analysis of networks involving rate of change with respect to time reduces to the study of graph differential equations and its associated matrix differential equations. In this paper we develop the Peano's and Picard's existence theorem for graph differential equations through its associated matrix differential equations.

 


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References


D.D.Siljak, Dynamic Graphs, Nonlinear Analysis, Hybrid systems 2(2008) 544-547.

V.Lakshmikantham and S.Leela, Differential and Integral Inequalities Theory and Applications. Academic Press, New York and London, 1969.

J.Vasundhara Devi, R.V.G Ravi Kumar, N.Giri Babu, On graph differential equations and its associated matrix differential equations Malaya Journal of Matematik 1 (1) (2013) 1-9.


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