Structure of a Parabolic Partial Differential Equation on Graphs and Digital spaces. Solution of PDE on Digital Spaces: a Klein Bottle, a Projective Plane, a 4D Sphere and a Moebius Band
arXiv:1701.05232 · doi:10.11648/j.dmath.20160101.12
Abstract
This paper studies the structure of a parabolic partial differential equation on graphs 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.
11-pages, 11 figures, accepted for publication in International Journal of Discrete Mathematics. arXiv admin note: text overlap with arXiv:1507.08109