Solving the Cauchy problem for a three-dimensional difference equation in a parallelepiped
Classical Analysis and ODEs
2022-02-01 v1 Mathematical Software
Numerical Analysis
Numerical Analysis
Abstract
The aim of this article is further development of the theory of linear difference equations with constant coefficients. We present a new algorithm for calculating the solution to the Cauchy problem for a three-dimensional difference equation with constant coefficients in a parallelepiped at the point using the coefficients of the difference equation and Cauchy data. The implemented algorithm is the next significant achievement in a series of articles justifying the Apanovich and Leinartas' theorems about the solvability and well-posedness of the Cauchy problem. We also use methods of computer algebra since the three-dimensional case usually demands extended calculations.
Cite
@article{arxiv.2201.13308,
title = {Solving the Cauchy problem for a three-dimensional difference equation in a parallelepiped},
author = {Marina S. Apanovich and Alexander P. Lyapin and Konstantin V. Shadrin},
journal= {arXiv preprint arXiv:2201.13308},
year = {2022}
}