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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2012, Issue 3(28), Pages 152–162 (Mi vsgtu1071)  

This article is cited in 1 scientific paper (total in 1 paper)

Calculus Mathematics

Modification of finite differences method with use of Taylor expansions

G. A. Pavlova, I. V. Belyaeva

Samara State Technical University, Samara, Russia

Abstract: The conducted research compares the method of Taylor expansions and the finite difference method. The obtained method of Taylor expansions employs three, four and five series terms. For each modification a finite difference scheme is presented and its stability, convergence, and approximation are analyzed. For both methods the number of arithmetic operations is counted and compared as well as an error. The advantages of the method of Taylor expansions are revealed.

Keywords: ordinary differential equations, boundary value problem, Taylor series, approximation, stability, convergence, finite difference method, method of Taylor expansions, numerical method

DOI: https://doi.org/10.14498/vsgtu1071

Full text: PDF file (179 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
References: PDF file   HTML file

Bibliographic databases:

UDC: 517.927:519.624
MSC: 34B99
Original article submitted 02/V/2012
revision submitted – 25/VII/2012

Citation: G. A. Pavlova, I. V. Belyaeva, “Modification of finite differences method with use of Taylor expansions”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 3(28) (2012), 152–162

Citation in format AMSBIB
\Bibitem{PavBel12}
\by G.~A.~Pavlova, I.~V.~Belyaeva
\paper Modification of finite differences method with use of~Taylor expansions
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2012
\vol 3(28)
\pages 152--162
\mathnet{http://mi.mathnet.ru/vsgtu1071}
\crossref{https://doi.org/10.14498/vsgtu1071}
\zmath{https://zbmath.org/?q=an:1326.65096}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. A. Usov, “Sposob resheniya kraevykh zadach s neyavnym primeneniem ryadov Teilora”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 4(29) (2012), 227–232  mathnet  crossref
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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