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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2012, Number 5, Pages 24–30 (Mi vmumm526)  
This article is cited in 11 scientific papers (total in 11 papers)

Mathematics

Calculation of expansion coefficients of series in Chebyshev polynomials for a solution to a Cauchy problem

O. B. Arushanyan, N. I. Volchenskova, S. F. Zaletkin

Lomonosov Moscow State University, Research Computing Center
Full-text PDF (242 kB) Citations (11)
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Abstract: Two approaches are proposed to determine an initial approximation for the coefficients of an expansion of the solution to a Cauchy problem for ordinary differential equations in the form of series in shifted Chebyshev polynomials of the first kind. This approximation is used in an analytical method to solve ordinary differential equations using orthogonal expansions.
Key words: ordinary differential equations, approximate analytical methods of integration, numerical methods of integration, orthogonal expansions, shifted Chebyshev polynomials, Markov quadrature formulas.
Funding agency Grant number
Russian Foundation for Basic Research 10-01-00297
Received: 08.11.2011
English version:
Moscow University Mathematics Bulletin, 2012, Volume 67, Issue 5-6, Pages 211–216
DOI: https://doi.org/10.3103/S0027132212050051
Bibliographic databases:
Document Type: Article
UDC: 519.622
Language: Russian
Citation: O. B. Arushanyan, N. I. Volchenskova, S. F. Zaletkin, “Calculation of expansion coefficients of series in Chebyshev polynomials for a solution to a Cauchy problem”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2012, no. 5, 24–30; Moscow University Mathematics Bulletin, 67:5-6 (2012), 211–216
Citation in format AMSBIB
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\jour Moscow University Mathematics Bulletin
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  • https://www.mathnet.ru/eng/vmumm/y2012/i5/p24
    • This publication is cited in the following 11 articles:
    1. O. B. Arushanyan, S. F. Zaletkin, “Approximate integration of the canonical systems of second order ordinary differential equations with the use of Chebyshev series with error estimation for solution and its derivative”, Moscow University Mathematics Bulletin, 77:4 (2022), 191–198  mathnet  crossref  mathscinet  zmath
    2. S. F. Zaletkin, “Approximate integration of ordinary differential equations using Chebyshev series with precision control”, Math. Models Comput. Simul., 15:1 (2023), 34–46  mathnet  crossref  crossref  mathscinet
    3. O. B. Arushanyan, S. F. Zaletkin, “Applying the method of integration of ordinary differential equations based on the Chebyshev series to the restricted plane circular three-body problem”, Moscow University Mathematics Bulletin, 76:3 (2021), 118–122  mathnet  crossref  mathscinet  zmath  isi
    4. O. B. Arushanyan, S. F. Zaletkin, “On the computation of approximate solution to ordinary differential equations by the Chebyshev series method and estimation of its error”, Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 75:5 (2020), 204–208  mathnet  crossref  mathscinet  zmath  isi
    5. O. B. Arushanyan, S. F. Zaletkin, “On some analytic method for approximate solution of systems of second order ordinary differential equations”, Moscow University Mathematics Bulletin, 74:3 (2019), 127–130  mathnet  crossref  mathscinet  zmath  isi
    6. O. B. Arushanyan, S. F. Zaletkin, “Justification of some approach to implementation of orthogonal expansions for approximate integration of canonical systems of second order ordinary differential equations”, Moscow University Mathematics Bulletin, 73:3 (2018), 111–115  mathnet  crossref  mathscinet  zmath  isi
    7. O. B. Arushanyan, S. F. Zaletkin, “Solvability of a system of equations for the Fourier-Chebyshev coefficients when solving ordinary differential equations by the Chebyshev series method”, Moscow University Mathematics Bulletin, 72:5 (2017), 213–216  mathnet  crossref  mathscinet  isi
    8. O. B. Arushanyan, S. F. Zaletkin, “The use of Chebyshev series for approximate analytic solution of ordinary differential equations”, Moscow University Mathematics Bulletin, 71:5 (2016), 212–215  mathnet  crossref  mathscinet  isi
    9. O. B. Arushanyan, N. I. Volchenskova, S. F. Zaletkin, “Application of Chebyshev series to integration of ordinary differential equations with rapidly growing solutions”, Moscow University Mathematics Bulletin, 70:5 (2015), 237–240  mathnet  crossref  mathscinet  isi
    10. O. B. Arushanyan, N. I. Volchenskova, S. F. Zaletkin, “On an approach to integration of ordinary differential equations with the use of series”, Moscow University Mathematics Bulletin, 69:6 (2014), 272–274  mathnet  crossref  mathscinet
    11. O. B. Arushanyan, N. I. Volchenskova, S. F. Zaletkin, “Primenenie ryadov Chebysheva dlya integrirovaniya obyknovennykh differentsialnykh uravnenii”, Sib. elektron. matem. izv., 11 (2014), 517–531  mathnet
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