This article is cited in 7 papers

Resolving sequences of operators for linear ordinary differential and difference systems of arbitrary order

S. A. Abramov^a, M. Petkovšek^b, A. A. Ryabenko<sup>a

a</sup> Federal Research Center “Computer Science and Control” of the Russian Academy of Science, Vavilova str., 40, Moscow, 119333, Russia
^b University of Ljubljana; Faculty of Mathematics and Physics, Jadranska 19, SI-1000, Ljubljana, Slovenia

Abstract: We introduce the notion of a resolving sequence of (scalar) operators for a given differential or difference system with coefficients in some differential or difference field K. We propose an algorithm to construct, such a sequence, and give some examples of the use of this sequence as a suitable auxiliary tool for finding certain kinds of solutions of differential and difference systems of arbitrary order. Some experiments with our implementation of the algorithm are reported.

Key words: higher-order linear systems of differential and difference equations resolving sequence of operators embracing system companion matrix cyclic vector hypergeometric solutions of difference systems formal exponential-logarithmic solutions of differential systems.

UDC: 519.7

Received: 01.09.2015
Revised: 21.10.2015

Language: English

DOI: 10.7868/S0044466916050033

 English version: Computational Mathematics and Mathematical Physics, 2016, 56:5, 894–910

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