Email this article METHOD FOR CHECKING THE REGULARITY OF A SINGULAR POINT OF A SYSTEM OF LINEAR DIFFERENTIAL EQUATIONS WITH MEROMORPHIC COEFFICIENTS
- Authors: Ilyukhin D.O.1, Parusnikova A.V.2
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Affiliations:
- State Budgetary Educational Institution “Bauman Engineering School” № 1580
- HSE University
- Issue: No 1 (2025)
- Pages: 5-9
- Section: COMPUTER ALGEBRA
- URL: https://journal-vniispk.ru/0132-3474/article/view/287074
- DOI: https://doi.org/10.31857/S0132347425010015
- EDN: https://elibrary.ru/DXVBZG
- ID: 287074
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Abstract
This paper proposes a program written in a symbolic computing package that allows one to check whether a singular point of a linear meromorphic system of arbitrary order is regular. The program is based on the known method for reducing this system by linear substitution to a linear differential equation with meromorphic coefficients.
Keywords
About the authors
D. O. Ilyukhin
State Budgetary Educational Institution “Bauman Engineering School” № 1580Moscow, Russia
A. V. Parusnikova
HSE University
Email: aparusnikova@hse.ru
Moscow, Russia
References
- Zoladek H. The monodromy group // Instytut matematyczny PAN. Basel: Birkhauser Verlag (2006).
- Moser J. The order of a singularity in Fuchs’ theory // Math Z. 1959. V. 72. P. 379–398.
- Barkatou A. A rational version of Moser’s algorithm // Proceedings of the 1995 international symposium on Symbolic and algebraic computation. April. 1995. P. 297–302.
- Bruno A.D. Meromorphic conductivity of a linear triangular system of ODEs, Dokl. Akad. Nauk, 2000, vol. 371, no. 5, pp. 587–590
- Vyugin I.V., Gontsov R.R. Additional parameters in inverse problems of monodromy, Sbornik: Mathematics, 2006, vol. 197, no. 12, pp. 1753–1773
- Ilyukhin D.O., Parusnikova A.V. Regularity criterion for linear systems of linear differential equations of small orders with meromorphic coefficients, Tr. Priokskoi nauchnoi konferentsii Differentsial’nye uravneniya i smezhnye voprosy matematiki (Proc. Priokskaya Sci. Conf. Differential Equations and Related Topics in Mathematics), 2019, pp. 65–73
- azov V. Asimptoticheskie razlozheniya reshenii obyknovennykh differentsial’nykh uravnenii (Asymptotic Expansions of Solutions of Ordinary Differential Equations), Moscow: Mir, 1968.
- Wolfram St. The Mathematica Book. Wolfram Media, Inc., 2003. 1488 p.
- Gromak V.I., Laine I., and Shimomura S. Painleve Differential Equations in the Complex Plane // De Gruyter Studies in Mathematics, vol. 28, Berlin, 2002.
- Lin Y., Dai D., Tibboel P. Existence and uniqueness of tronquee solutions of the third and fourth Painleve equations // Nonlinearity. 2014. Vol. 27. No. 2. P. 171–186.
- Parusnikova A.V., Vasilyev A.V. On the exact Gevrey order of formal Puiseux series solutions to the third Painleve equation // Journal of Dynamical and Control Systems. 2019. Vol. 25. No. 4. P. 681–690.
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