Abstract
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.
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Dudgeon, D.E. and Mersereau, R.M., Multidimensional Digital Signal Processing, Prentice Hall, 1983.
Isermann, R., Digital Control Systems, Springer, 1981.
Ryaben'kii, V.S., Vvedenie v vychislitel’nuyu matematiku (Introduction to Computational Mathematics), Moscow: FIZMATLIT, 2000, 2nd ed.
Stanley, R.P., Enumerative Combinatorics: Volume 1, Cambridge University Press, 2011, 2nd ed.
Stanley, R.P., Enumerative Combinatorics: Volume 2, Cambridge University Press, 1999.
Lyapin, A.P., Riordan sequences and two-dimensional difference equations, Journal of Siberian Federal University. Mathematics & Physics., 2009, vol. 2, no. 2, pp. 210–220.
Kytmanov, A.A., Lyapin, A.P., and Sadykov, T.M., Evaluating the rational generating function for the solution of the Cauchy problem for a two-dimensional difference equation with constant coefficients, Program. Comput. Software, 2017, vol. 43, pp. 105–111.
Apanovich, M.S., Lyapin, A.P., and Shadrin, K.V., Solving the Cauchy problem for a two-dimensional difference equation at a point using computer algebra methods, Program. Comput. Software, 2021, vol. 47, pp. 1–5.
Rogozina, M.S., Solvability of the Cauchy difference problem for multilayer implicit difference schemes, Vestn. Sib. Gos. Aerosp. Univ., Mat., Mekh., Inf., 2014, vol. 55, no. 3, pp. 126–130.
Iokhvidov, I.S., Gankelevy i teplitsevy matritsy (Hankel and Toeplitz Matrices), Moscow: Nauka, 1974.
Apanovich, M.S., Lyapin, A.P., and Shadrin, K.V., Computing the sequence of principal minors of a banded Toeplitz matrix, Prikl. Mat. Fiz. (Appl. Math. & Phys.), 2020, vol. 52, no. 1, pp. 5–10.
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This work was supported by the Krasnoyarsk Mathematical Center and financed by the Ministry of Science and Higher Education of the Russian Federation in the framework of the establishment and development of regional Centers for Mathematics Research and Education (agreement no. 075-02-2022-876).
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Apanovich, M.S., Lyapin, A.P. & Shadrin, K.V. Algorithm for Solving the Cauchy Problem for a Two-Dimensional Difference Equation with Initial Data Defined in a “Strip”. Program Comput Soft 48, 286–292 (2022). https://doi.org/10.1134/S0361768822040028
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DOI: https://doi.org/10.1134/S0361768822040028