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 Num. Meth. Prog., 2005, Volume 6, Issue 3, Pages 1–17 (Mi vmp661)

Markov's formula with two fixed nodes for numerical integration and its application in orthogonal expansions

S. F. Zaletkin

Lomonosov Moscow State University, Research Computing Center

Abstract: Some properties of Chebyshev's series are discussed. These series are used as a basis for constructing numerical analytical methods of solving Cauchy problems for systems of ordinary differential equations. Particular attention is given to the calculation of Chebyshev's coefficients with the aid of numerical integration. A Markov quadrature formula with two fixed nodes and the weight function that corresponds to the orthogonal system of Chebyshev's shifted polynomials of the first kind is derived. Some properties of partial sums of Chebyshev's series with the coefficients obtained by Markov's formula are described.

Keywords: Markov quadrature formulas, Chebyshev's series, ordinary differential equations, Cauchy problem.

Full text: PDF file (206 kB)
UDC: 519.644.2:519.651

Citation: S. F. Zaletkin, “Markov's formula with two fixed nodes for numerical integration and its application in orthogonal expansions”, Num. Meth. Prog., 6:3 (2005), 1–17

Citation in format AMSBIB
\Bibitem{Zal05} \by S.~F.~Zaletkin \paper Markov's formula with two fixed nodes for numerical integration and its application in orthogonal expansions \jour Num. Meth. Prog. \yr 2005 \vol 6 \issue 3 \pages 1--17 \mathnet{http://mi.mathnet.ru/vmp661} 

• http://mi.mathnet.ru/eng/vmp661
• http://mi.mathnet.ru/eng/vmp/v6/i3/p1

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. 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
2. 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
3. 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
4. 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