Abstract

An algorithm for finding the solution to the Cauchy problem for a two-dimensional difference equation with constant coefficients at a point using computer algebra is described. In the one-dimensional case, solving the Cauchy problem is easy; however, already in the two-dimensional case the number of unknowns rapidly increases at each step. To automate the process of computing the solution to the Cauchy problem for a two-dimensional difference equation with constant coefficients at a given point, an algorithm in MATLAB is developed in which the input data are the matrix of coefficients obtained on the basis of the structure of the two-dimensional polynomial difference equation, coordinates of the points that specify the structure and the size of the matrix of initial data, and the matrix of the initial data. The algorithm produces the solution to the Cauchy problem for the given two-dimensional difference equation at the given point.

中文翻译：

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使用计算机代数方法求解二维差分方程在点处的柯西问题

摘要

描述了一种使用计算机代数在点处具有恒定系数的二维差分方程的柯西问题的解的算法。在一维情况下，解决柯西问题很容易。但是，在二维情况下，未知数在每一步都迅速增加。为了使给定点处具有常数系数的二维差分方程的柯西问题的求解的计算过程自动化，开发了一种MATLAB算法，其中输入数据是基于结构获得的系数矩阵二维多项式差分方程的坐标，表示初始数据矩阵的结构和大小以及初始数据矩阵的点的坐标。