Solving the Cauchy problem for a three-dimensional difference equation in a parallelepiped

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 poin...

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Bibliographic Details
Published inarXiv.org
Main Authors Apanovich, Marina S, Lyapin, Alexander P, Shadrin, Konstantin V
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 09.01.2022
Subjects
Algorithms
Cauchy problems
Coefficients
Computer algebra
Difference equations
Mathematical analysis
Parallelepipeds
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Summary: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.
ISSN:2331-8422