Procedures for searching local solutions of linear differential systems with infinite power series in the role of coefficients
- Authors: Abramov S.A.1, Ryabenko A.A.1, Khmelnov D.E.1
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Affiliations:
- Dorodnicyn Computing Center
- Issue: Vol 42, No 2 (2016)
- Pages: 55-64
- Section: Article
- URL: https://journals.rcsi.science/0361-7688/article/view/176408
- DOI: https://doi.org/10.1134/S036176881602002X
- ID: 176408
Cite item
Abstract
Construction of Laurent, regular, and formal (exponential–logarithmic) solutions of full-rank linear ordinary differential systems is discussed. The systems may have an arbitrary order, and their coefficients are formal power series given algorithmically. It has been established earlier that the first two problems are algorithmically decidable and the third problem is not decidable. A restricted variant of the third problem was suggested for which the desired algorithm exists. In the paper, a brief survey of algorithms for the abovementioned decidable problems is given. Implementations of these algorithms in the form of Maple procedures with a uniform interface and data representation are suggested.
About the authors
S. A. Abramov
Dorodnicyn Computing Center
Author for correspondence.
Email: sergeyabramov@mail.ru
Russian Federation, ul. Vavilova 40, Moscow, 119333
A. A. Ryabenko
Dorodnicyn Computing Center
Email: sergeyabramov@mail.ru
Russian Federation, ul. Vavilova 40, Moscow, 119333
D. E. Khmelnov
Dorodnicyn Computing Center
Email: sergeyabramov@mail.ru
Russian Federation, ul. Vavilova 40, Moscow, 119333