Algorithm for Solving the Cauchy Problem for a Two-Dimensional Difference Equation with Initial Data Defined in a "Strip".

In this paper, we propose an algorithm for solving the Cauchy problem for a two-dimensional difference equation with constant coefficients at a point, based on its coefficients and the initial data for the Cauchy problem, which are defined in a "strip." For this purpose, computer algebra methods are employed. To automate the process of computing the solution, the algorithm is implemented in MATLAB, with the input data being the matrix of coefficients of the two-dimensional polynomial difference equation, the coordinates of the initial data matrix (which defines the structure of the difference equation), and the coordinates of the point that determines the dimension of the initial data matrix. The output of the algorithm is a solution of the Cauchy problem (with the initial data defined in a "strip") for the two-dimensional difference equation, which is a function value at the desired point. [ABSTRACT FROM AUTHOR]