Parabolic equations on digital spaces. Solutions on the digital Moebius strip and the digital projective plane

TL;DR

This paper introduces a parabolic equation on digital spaces, specifically on the digital Moebius strip and projective plane, and explores solutions relevant to engineering applications like airplane wings.

Contribution

It defines a new parabolic equation on digital spaces and analyzes solution methods, including matrix and separation of variables, for complex geometries.

Findings

Exact solutions exist under certain conditions.

Numerical solutions demonstrated on digital Moebius strip.

Applicable to mechanical and aerodynamic property analysis.

Abstract

In this work, we define a parabolic equation on digital spaces and study its properties. The equation can be used in investigation of mechanical, aerodynamic, structural and technological properties of a Moebius strip, which is used as a basic element of a new configuration of an airplane wing. Condition for existence of exact solutions by a matrix method and a method of separation of variables are studied and determined. As examples, numerical solutions on Moebius strip and projective plane are presented.