On graph differential equations and its associated matrix differential equations

J. Vasundhara Devi; R.V.G. Ravi Kumar; N. Giribabu

doi:10.26637/mjm101/001

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 differential 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 differential equation is developed.

Keywords:

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

Mathematics Subject Classification:

34G20

Authors Imprint References Funding Related Articles Downloads

J. Vasundhara Devi GVP-Prof.V.Lakshmikantham Institute for Advanced Studies, Department of Mathematics, GVP College of Engineering, Visakhapatnam-530048, Andhra Pradesh, India. https://orcid.org/0000-0001-9616-5077
R.V.G. Ravi Kumar GVP-Prof.V.Lakshmikantham Institute for Advanced Studies, Department of Mathematics, GVP College of Engineering, Visakhapatnam-530048, Andhra Pradesh, India.
N. Giribabu GVP-Prof.V.Lakshmikantham Institute for Advanced Studies, Department of Mathematics, GVP College of Engineering, Visakhapatnam-530048, Andhra Pradesh, India.

Pages: 1-9
Date Published: 01-01-2013
Vol. 1 No. 01 (2013): Malaya Journal of Matematik (MJM)

Narsingh Deo, Graph Theory with Application to Engineering and Computer Science, 2000.

D.D.Siljak, Dynamic graphs, Nnlinear Analysis: Hybrid Systems 2(2008) 544-567. DOI: https://doi.org/10.1016/j.nahs.2006.08.004

G.S.Ladde, V.Lakshmikantham and A.S. Vatsala, Monotone Iterative Techniques for Nonlinear Differential Equations, Pitman Publishing INC., 1985.

A.R. Radcliffe-Brown, On social structure, Journal of the Royal Anthropological Institute of Great Britain and Ireland 70(1940)1-12. DOI: https://doi.org/10.2307/2844197