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Zh. Vychisl. Mat. Mat. Fiz., 2015, Volume 55, Number 11, Pages 1827–1834 (Mi zvmmf10294)  

This article is cited in 2 scientific papers (total in 2 papers)

A numerical method for solving systems of nonlinear equations

A. A. Abramovab, L. F. Yukhnocd

a Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141700, Russia
b Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia
c Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4a, Moscow, 125047, Russia
d National Research Nuclear University, Kashirskoe sh. 31, Moscow, 115409, Russia

Abstract: Under certain conditions on nonlinear equations in a real finite-dimensional space, a numerical method for solving such equations is proposed. The method is based on the use of an auxiliary differential equation. A fairly rough approximate solution to this equation can be refined by applying Newton's method to the original problem. The result produced by the auxiliary equation is automatically a good initial approximation for Newton’s method. This combination ensures that the original problem can be solved to the required accuracy starting from any initial approximation.

Key words: system of nonlinear equations, Newton's method, Hadamard existence theorem.

DOI: https://doi.org/10.7868/S0044466915110022

Full text: PDF file (98 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2015, 55:11, 1794–1801

Bibliographic databases:

UDC: 519.624
MSC: 65H10
Received: 21.04.2015

Citation: A. A. Abramov, L. F. Yukhno, “A numerical method for solving systems of nonlinear equations”, Zh. Vychisl. Mat. Mat. Fiz., 55:11 (2015), 1827–1834; Comput. Math. Math. Phys., 55:11 (2015), 1794–1801

Citation in format AMSBIB
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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. V. Arutyunov, “On the existence of solutions of nonlinear equations”, Dokl. Math., 95:1 (2017), 46–49  crossref  mathscinet  zmath  isi
    2. L. F. Petrov, “Search for periodic solutions of highly nonlinear dynamical systems”, Comput. Math. Math. Phys., 58:3 (2018), 384–393  mathnet  crossref  crossref  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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