Periodic boundary value problem for the graph differential equation and the matrix differential equation

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DOI:

https://doi.org/10.26637/mjm304/018

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 monotone iterative technique for graph differential equations and its associated matrix differential equations using Periodic boundary value problem.

Keywords:

Graph differential equation, Matrix differential equation, coupled lower and upper solutions, 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-530 048, India.
  • S.Srinivasa Rao GVP-Prof.V.Lakshmikantham Institute for Advanced Studies, Department of Mathematics, GVP College of Engineering, Visakhapatnam-530 048, India.
  • I.S.N.R.G.Bharat GVP-Prof.V.Lakshmikantham Institute for Advanced Studies, Department of Mathematics, GVP College of Engineering, Visakhapatnam-530 048, India.
  • Pages: 598-606
  • Date Published: 01-10-2015
  • Vol. 3 No. 04 (2015): Malaya Journal of Matematik (MJM)

D.D.Siljak, Dynamic Graphs, Nonlinear Analysis, Hybrid systems 2(2008) 544-547. DOI: https://doi.org/10.1016/j.nahs.2006.08.004

J.Vasundhara Devi, R.V.G Ravi Kumar, N.Giri Babu, On graph differential equations and its associated matrix differential equations, Malaya Journa of Mathematik 1 (1) (2012) 82-90. DOI: https://doi.org/10.26637/mjm101/001

G.S.Ladde,V. Lakshmikantham, A.S.Vatsala, Monotone iterative techniques for nonlinear differential equations, Pitman publishing ltd, 1985.

J.Vasundhara Devi, R.V.G Ravi Kumar, Modeling the prey predator problem by a graph differential equations, European Journal of Pure and Applied Mathematics Vol.7, No. 1, 2014, 37-44.

S.G.Pandit, D.H.Dezern and J.O.Adeyeye, Periodic boundary value problems for nonlinear integro differential equations, Proceedings ofNeural, Parallel, and Scientific Computations vol 4, pp :316320,Dynamic, Atlanta, Ga, USA, 2010.

M. Sokol and A.S. Vatsala, A unified exhaustive study of monotone iterative method for initial value problems, NonlinearStudies 8 (4), 429-438, (2001).

I. H. West and A. S. Vatsala. Generalized monotone iterative method for integro differential equations with periodic boundary conditions. Math. Inequal. Appl., 10 : 151-163, 2007. DOI: https://doi.org/10.7153/mia-10-13

Wen-Li Wang and Jing-Feng Tian, Generalized monotone iterative method for nonlinear boundary value

problems with causal operators, Boundary Value Problems (Accepted).

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Published

01-10-2015

How to Cite

J. Vasundhara Devi, S.Srinivasa Rao, and I.S.N.R.G.Bharat. “Periodic Boundary Value Problem for the Graph Differential Equation and the Matrix Differential Equation”. Malaya Journal of Matematik, vol. 3, no. 04, Oct. 2015, pp. 598-06, doi:10.26637/mjm304/018.