平行六面体上三维差分方程Cauchy问题的求解
Solving the Cauchy problem for a three-dimensional difference equation in a parallelepiped
摘要：
本文的目的是进一步发展常系数线性差分方程的理论。本文提出了一种利用差分方程的系数和Cauchy数据计算平行六面体上的三维常系数差分方程的Cauchy问题解的新算法。实现的算法是证明Apanovich和Leinartas关于柯西问题的可解性和适定性的定理的一系列文章中的下一个重要成就。我们还使用计算机代数的方法，因为三维的情况下，通常需要扩展的计算。
英文摘要：
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.
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