We present an efficient algorithm for the construction of a fundamental system of solutions of a linear finite-order difference equation. We obtain expressions in which all elements of this system are expressed via one of its elements and find a particular solution of an inhomogeneous equation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. K. Godunov and V. S. Ryaben’kii, Difference Schemes [in Russian], Nauka, Moscow (1977).
D. I. Martynyuk, Lectures on the Qualitative Theory of Difference Equations [in Russian], Naukova Dumka, Kiev (1972).
V. K. Romanenko, Difference Equations [in Russian], Binom, Moscow (2006).
V. E. Kruglov, “Construction of a fundamental system of solutions of a linear difference equation of order n,” in: Abstracts of the Conference “Contemporary Problems of Mechanics and Mathematics” [in Ukrainian], Vol. 3, Lviv (2008), pp. 69–71.
J. Wimp, Computation with Recurrence Relations, Pitman, Boston (1984).
A. O. Gel’fond, Calculus of Finite Differences [in Russian], Nauka, Moscow (1967).
V. E. Kruglov, “Solution of a second-order Poincaré–Perron-type equation and differential equations that can be reduced to it,” Ukr. Mat. Zh., 60, No. 7, 900–917 (2008).
I. I. Gikhman, A. V. Skorokhod, and M. I. Yadrenko, Probability Theory and Mathematical Statistics [in Russian], Vyshcha Shkola, Kiev (1988).
N. N. Vorob’ev, Fibonacci Numbers [in Russian], Nauka, Moscow (1983).
Author information
Authors and Affiliations
Additional information
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 6, pp. 777 – 794, June, 2009.
Rights and permissions
About this article
Cite this article
Kruglov, V.E. Construction of a fundamental system of solutions of a linear finite-order difference equation. Ukr Math J 61, 923–944 (2009). https://doi.org/10.1007/s11253-009-0255-4
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-009-0255-4