Solution of the Hyperbolic Partial Differential Equation on Graphs and Digital Spaces: a Klein Bottle a Projective Plane and a 4D Sphere

05/01/2017
by   Alexander V. Evako, et al.
0

In many cases, analytic solutions of partial differential equations may not be possible. For practical problems, it is more reasonable to carry out computational solutions. However, the standard grid in the finite difference approximation is not a correct model of the continuous domain in terms of digital topology. In order to avoid serious problems in computational solutions it is necessary to use topologically correct digital domains. This paper studies the structure of the hyperbolic partial differential equation on graphs and digital n-dimensional manifolds, which are digital models of continuous n-manifolds. Conditions for the existence of solutions are determined and investigated. Numerical solutions of the equation on graphs and digital n-manifolds are presented.

READ FULL TEXT

Authors

page 1

page 2

page 3

page 4

01/20/2022

Finite difference and finite element methods for partial differential equations on fractals

In this paper, we present numerical procedures to compute solutions of p...
08/26/2020

A general framework for substructuring-based domain decomposition methods for models having nonlocal interactions

A rigorous mathematical framework is provided for a substructuring-based...
07/10/2020

Algorithmic differentiation of hyperbolic flow problems

We are interested in the development of an algorithmic differentiation f...
06/04/2011

Optimal Reinforcement Learning for Gaussian Systems

The exploration-exploitation trade-off is among the central challenges o...
04/16/2019

Unification and combination of iterative insertion strategies with one-step traversals

Motivated by an ongoing project on the computer aided derivation of mult...
03/03/2017

Computer-assisted proof of heteroclinic connections in the one-dimensional Ohta-Kawasaki model

We present a computer-assisted proof of heteroclinic connections in the ...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.