Abstract
In this paper, we investigate the generalized partial difference operator and propose a model of it in discrete heat equation with several parameters and shift values. The diffusion of heat is studied by the application of Fourier’s law of heat conduction in dimensions up to three and several solutions are postulated for the same. Through numerical simulations using MATLAB, solutions are validated and applications are derived.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ablowitz, M.J., Ladik, J.F.: On the solution of a class of nonlinear partial difference equations. Stud. Appl. Math. 57, 1–12 (1977)
Xavier, G.B.A., Gerly, T.G., Begum, H.N.: Finite Series of Polynomials and Polynomial Factorials arising from Generalized q-Difference operator. Far East J. Math. Sci. 94(1), 47–63 (2014)
Bastos, N.R.O., Ferreira, R.A.C., Torres, D.F.M.: Discrete-time fractional variational problems. Signal Process. 91(3), 513–524 (2011)
Ferreira, R.A.C., Torres, D.F.M.: Fractional h-difference equations arising from the calculus of variations. Appl. Anal. Discret. Math. 5(1), 110–121 (2011)
Cheng, S.S.: Sturmian comparison theorems for three term recurrence equations. J. Math. Anal. Appl. 111, 464–474 (1985)
Popenda, J., Szmanda, B.: On the oscillation of solutions of certain difference equations. Demonstratio Mathematica XVII(1), 153–164 (1984)
Koshy, T.: Fibonacci and Lucas Numbers with Applications. Wiley-Interscience, New York (2001)
Manuel, M.M.S., Chandrasekar, V., Xavier, G.B.A.: Solutions and applications of certain class of \(\alpha \)- difference equations. Int. J. Appl. Math. 24(6), 943–954 (2011)
Miller, K.S., Ross, B.: Fractional Difference Calculus in Univalent Functions, pp. 139–152. Horwood, UK (1989)
Manuel, M.S., Xavier, G.B.A., Chandrasekar, V., Pugalarasu, R.: Theory and application of the Generalized Difference Operator of the \(n^{th}\) kind(Part I). Demonstratio Mathematica 45(1), 95–106 (2012)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Xavier, G.B.A., Borg, S.J., Meganathan, M. (2018). Discrete Heat Equation with Shift Values. In: Pinelas, S., Caraballo, T., Kloeden, P., Graef, J. (eds) Differential and Difference Equations with Applications. ICDDEA 2017. Springer Proceedings in Mathematics & Statistics, vol 230. Springer, Cham. https://doi.org/10.1007/978-3-319-75647-9_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-75647-9_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-75646-2
Online ISBN: 978-3-319-75647-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)