Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2016, Number 5, Pages 52–56 (Mi vmumm182)  
This article is cited in 3 scientific papers (total in 3 papers)

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The use of Chebyshev series for approximate analytic solution of ordinary differential equations

O. B. Arushanyan, S. F. Zaletkin

Lomonosov Moscow State University, Research Computing Center
Full-text PDF (292 kB) Citations (3)
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Abstract: Application of Chebyshev series to solve ordinary differential equations is described. This approach is based on the approximation of the solution to a given Cauchy problem and its derivatives by partial sums of shifted Chebyshev series. The coefficients of the series are determined by an iterative process using Markov quadrature formulas. It is shown that the proposed approach can be applied to formulate an approximate analytical method for solving Cauchy problems. A number of examples are considered to illustrate the obtaining of approximate analytical solutions in the form of partial sums of shifted Chebyshev series.
Key words: ordinary differential equations, approximate analytical methods, numerical methods, orthogonal expansions, shifted Chebyshev series, Markov quadrature formulas.
Received: 14.03.2016
English version:
Moscow University Mathematics Bulletin, 2016, Volume 71, Issue 5, Pages 212–215
DOI: https://doi.org/10.3103/S0027132216050089
Bibliographic databases:
Document Type: Article
UDC: 519.622
Language: Russian
Citation: O. B. Arushanyan, S. F. Zaletkin, “The use of Chebyshev series for approximate analytic solution of ordinary differential equations”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2016, no. 5, 52–56; Moscow University Mathematics Bulletin, 71:5 (2016), 212–215
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/vmumm/y2016/i5/p52
    • This publication is cited in the following 3 articles:
    1. N. D. Zolotareva, “On the recalculation of ellipsoids in estimating the error of the implicit Stormer method for a second-order linear differential equation”, Russian Universities Reports. Mathematics, 29:148 (2024), 391–400  mathnet  mathnet  crossref
    2. 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
    3. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Full-text PDF :77
    References:42
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