Volume 1, Issue 1, December 2016, Page: 5-14
Solution of a Parabolic Partial Differential Equation on Digital Spaces: A Klein Bottle, a Projective Plane, a 4D Sphere and a Moebius Band
Alexander V. Evako, Laboratory of Digital Technologies, Moscow, Russia
Received: Oct. 8, 2016;       Accepted: Nov. 17, 2016;       Published: Dec. 27, 2016
DOI: 10.11648/j.dmath.20160101.12      View  2813      Downloads  124
Abstract
This paper studies a parabolic partial differential equation on digital spaces and digital n-dimensional manifolds, which are digital models of continuous n-manifolds. Conditions for the existence of solutions of equations are determined and investigated. Numerical solutions of the equation on a Klein bottle, a projective plane, a 4D sphere and a Moebius strip are presented.
Keywords
Digital Surface, Graph, Parabolic PDE, Digital Topology, Moebius Strip, Klein Bottle, Projective Plane
To cite this article
Alexander V. Evako, Solution of a Parabolic Partial Differential Equation on Digital Spaces: A Klein Bottle, a Projective Plane, a 4D Sphere and a Moebius Band, International Journal of Discrete Mathematics. Vol. 1, No. 1, 2016, pp. 5-14. doi: 10.11648/j.dmath.20160101.12
Copyright
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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