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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2016, Volume 56, Number 5, Page 909
DOI: https://doi.org/10.7868/S0044466916050033 (Mi zvmmf10395) 		 
This article is cited in 6 scientific papers (total in 6 papers)

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

S. A. Abramova, M. Petkovšekb, A. A. Ryabenkoa

a 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
Full-text PDF (44 kB) Citations (6)
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DOI: https://doi.org/10.7868/S0044466916050033
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.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00174_а
Ministry of Education, Science and Sport of Slovenia Pl-0294
Supported in part by the Ministry of Education, Science and Sport of Slovenia research programme Pl-0294.
Received: 01.09.2015
Revised: 21.10.2015
English version:
Computational Mathematics and Mathematical Physics, 2016, Volume 56, Issue 5, Pages 894–910
DOI: https://doi.org/10.1134/S096554251605002X
Bibliographic databases:
Document Type: Article
UDC: 519.7
Language: English
Citation: S. A. Abramov, M. Petkovšek, A. A. Ryabenko, “Resolving sequences of operators for linear ordinary differential and difference systems of arbitrary order”, Zh. Vychisl. Mat. Mat. Fiz., 56:5 (2016), 909; Comput. Math. Math. Phys., 56:5 (2016), 894–910
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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