On graph differential equations and its associated matrix differential equations

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DOI:

https://doi.org/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
  • 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)

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Published

01-01-2013

How to Cite

J. Vasundhara Devi, R.V.G. Ravi Kumar, and N. Giribabu. “On Graph Differential Equations and Its Associated Matrix Differential Equations”. Malaya Journal of Matematik, vol. 1, no. 01, Jan. 2013, pp. 1-9, doi:10.26637/mjm101/001.

Issue

Vol. 1 No. 01 (2013): Malaya Journal of Matematik (MJM)

Section

Articles

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Copyright (c) 2013 MJM

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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