Abstract:
We previously published algorithms for searching the so-called Laurent and regular solutions of linear ordinary differential equations with infinite formal power series in the role of coefficients. The question of infinite series representation is very important for computer algebra. In those algorithms the series are given in truncated form, which means that we do not have complete information about the equation under consideration. Based on this incomplete information, algorithms give the maximum possible number of terms of the series included in the solutions. We are interested in the information about these solutions that is invariant to possible prolongations of those truncated series that represent the coefficients of the equation. The mentioned publications reported preliminary (trial) versions for procedures, which implement these algorithms, as well as experiments with them. To date, the procedures have been improved, the interface and data presentation are designed for them in a uniform manner. The advanced procedures are discussed in the current paper. The various examples are presented which illustrates the use of the procedures, including their optional parameters. These procedures are available from the web page http://www.ccas.ru/ca/TruncatedSeries.
Keywords:
truncated power series, linear ordinary differential equations, Laurent solutions, regular solutions, computer algebra, Maple.
The study was partially supported by RFBR, grant 19-01-00032
Document Type:
Article
Language: Russian
Citation:
S. A. Abramov, D. E. Khmelnov, A. A. Ryabenko, “Procedures to search for Laurent and regular solutions of linear ordinary differential equations with truncated power series coefficients”, Proceedings of ISP RAS, 31:5 (2019), 233–247
\Bibitem{AbrKhmRya19}
\by S.~A.~Abramov, D.~E.~Khmelnov, A.~A.~Ryabenko
\paper Procedures to search for Laurent and regular solutions of linear ordinary differential equations with truncated power series coefficients
\jour Proceedings of ISP RAS
\yr 2019
\vol 31
\issue 5
\pages 233--247
\mathnet{http://mi.mathnet.ru/tisp466}
\crossref{https://doi.org/10.15514/ISPRAS-2019-31(5)-17}
Linking options:
https://www.mathnet.ru/eng/tisp466
https://www.mathnet.ru/eng/tisp/v31/i5/p233
This publication is cited in the following 4 articles:
A. A. Panferov, E. A. Bordachenkova, “Strongly Cyclic Vectors”, Program Comput Soft, 51:2 (2025), 93
S. A. Abramov, A. A. Ryabenko, D. E. Khmelnov, “Counterexamples to the assumption on the possibility of prolongation of truncated solutions of a truncated LODE”, Comput. Math. Math. Phys., 63:1 (2023), 69–76
S. A. Abramov, A. A. Ryabenko, D. E. Khmelnov, “Searching for Laurent Solutions of Systems of Linear Differential Equations with Truncated Power Series in the Role of Coefficients”, Programmirovanie, 2023, no. 5, 35
S. A. Abramov, A. A. Ryabenko, D. E. Khmelnov, “Truncated series and formal exponential-logarithmic solutions of linear ordinary differential equations”, Comput. Math. Math. Phys., 60:10 (2020), 1609–1620
Citation in format AMSBIB
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