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Programming and Computer Software
Erschienen in: Programming and Computer Software 5/2023

01.10.2023

Searching for Laurent Solutions of Systems of Linear Differential Equations with Truncated Power Series in the Role of Coefficients

verfasst von: S. A. Abramov, A. A. Ryabenko, D. E. Khmelnov

Erschienen in: Programming and Computer Software | Ausgabe 5/2023

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Abstract

Systems of linear ordinary differential equations with the coefficients in the form of infinite formal power series are considered. The series are represented in a truncated form, with the truncation degree being different for different coefficients. Induced recurrent systems and literal designations for unspecified coefficients of the series are used as a tool for studying such systems. An algorithm for constructing Laurent solutions of the system is proposed for the case where the determinant of the leading matrix of the induced system is not zero and does not contain literals. The series included in the solutions are still truncated. The algorithm finds the maximum possible number of terms of the series that are invariant with respect to any prolongations of the truncated coefficients of the original system. The implementation of the algorithm as a Maple procedure and examples of its usage are presented.
Vorheriger Artikel Application of Computer Simulation to the Anonymization of Personal Data: Synthesis-Based Anonymization Model and Algorithm
Nächster Artikel On Implementation of Numerical Methods for Solving Ordinary Differential Equations in Computer Algebra Systems

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Literatur
1.
Abramov, S.A., Barkatou, M.A., and Khmelnov, D.E., On full rank differential systems with power series coefficients, J. Symbolic Comput., 2015, vol. 68, pp. 120–137.MathSciNetCrossRefMATH
2.
Abramov, S.A. and Khmelnov, D.E., Regular solutions of linear differential systems with power series coefficients, Program. Comput. Software, 2014, vol. 40, no. 2, pp. 98–105.MathSciNetCrossRefMATH
3.
Ryabenko, A.A. On exponential–logarithmic solutions of linear differential systems with power series coefficients, Program. Comput. Software, 2015, vol. 41, no. 2, pp. 112–118.MathSciNetCrossRefMATH
4.
Abramov, S.A., Ryabenko, A.A., and Khmelnov, D.E., Linear ordinary differential equations and truncated series, Comput. Math. Math. Phys., 2019, vol. 59, pp. 1649–1659.MathSciNetCrossRefMATH
5.
Abramov, S.A., Ryabenko, A.A., and Khmelnov, D.E., Regular solutions of linear ordinary differential equations and truncated series, Comput. Math. Math. Phys., 2020, vol. 60, pp. 1–14.MathSciNetCrossRefMATH
6.
Abramov, S.A., Ryabenko, A.A., and Khmelnov, D.E., Truncated series and formal exponential–logarithmic solutions of linear ordinary differential equations, Comput. Math. Math. Phys., 2020, vol. 60, no. 10, pp. 1609–1620.MathSciNetCrossRefMATH
7.
Abramov, S.A., Barkatou, M.A., and Pfluegel, E., Higher-order linear differential systems with truncated coefficients, Proc. of CASC’, 2011, pp. 10–24.
8.
Abramov, S.A. and Barkatou, M.A., On strongly non-singular polynomial matrices, Advances in Computer Algebra, Schneider, C. and Zima, E., Eds., Springer Proceedings in Mathematics & Statistics. 2018, vol. 226, pp. 1–17.MATH
9.
Abramov, S.A., Ryabenko, A.A., and Khmelnov, D.E., Procedures for searching Laurent and regular solutions of linear differential equations with the coefficients in the form of truncated power series, Program. Comput. Software, 2020, vol. 46, pp. 67–75.MathSciNetCrossRefMATH
10.
Maple online help. http://​www.​maplesoft.​com/​support/​help.​
11.
Abramov, S.A., Khmelnov, D.E., and Ryabenko, A.A., Truncated and infinite power series in the role of coefficients of linear ordinary differential equations, Lect. Notes Comput. Sci., 2020, vol. 12291, pp. 63–76.MathSciNetCrossRefMATH
12.
Abramov, S.A., Khmelnov, D.E., and Ryabenko, A.A., The TruncatedSeries package for solving linear ordinary differential equations having truncated series coefficients, Maple in Mathematics Education and Research, Springer Nature Switzerland, 2021, pp. 19–33.
13.
Abramov, S.A., Ryabenko, A.A., and Khmelnov, D.E., Procedures for constructing truncated solutions of linear differential equations with infinite and truncated power series in the role of coefficients, Program. Comput. Software, 2021, vol. 47, pp. 144–152.MathSciNetCrossRefMATH
14.
Abramov, S.A., Ryabenko, A.A., and Khmelnov, D.E., Procedures for searching local solutions of linear differential systems with infinite power series in the role of coefficients, Program. Comput. Software, 2016, vol. 42, pp. 55–64.MathSciNetCrossRefMATH
15.
Metadaten
Titel
Searching for Laurent Solutions of Systems of Linear Differential Equations with Truncated Power Series in the Role of Coefficients
verfasst von
S. A. Abramov
A. A. Ryabenko
D. E. Khmelnov
Publikationsdatum
01.10.2023
Verlag
Pleiades Publishing
Erschienen in
Programming and Computer Software / Ausgabe 5/2023
Print ISSN: 0361-7688
Elektronische ISSN: 1608-3261
DOI
https://doi.org/10.1134/S0361768823020020

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