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Zh. Vychisl. Mat. Mat. Fiz., 2005, Volume 45, Number 9, Pages 1580–1586 (Mi zvmmf595)  

On approximate projecting on a stable manifold

A. A. Kornev, A. V. Ozeritskii

Department of Mathematics and Mechanics, Moscow State University, Moscow, 119992, Russia

Abstract: For an element of a Banach space that belongs to a neighborhood of a fixed point of the given resolving operator, the problem of projecting on the corresponding stable manifold is examined. The projector is specified by a basis that describes the admissible modifications. The original problem is reduced to solving a nonlinear equation of a special form. Under the conventional assumptions, the solvability of this equation is proved. It is shown that the proposed method is locally equivalent to the well-known methods for approximating the stable manifold. The high efficiency of the method is demonstrated by the numerical experiments. Their results for the two-dimensional Chafe–Infant equation are presented.

Key words: Hadamard–Perron theorem, stable manifold, numerical algorithm.

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English version:
Computational Mathematics and Mathematical Physics, 2005, 45:9, 1525–1530

Bibliographic databases:
UDC: 519.62
Received: 30.12.2004

Citation: A. A. Kornev, A. V. Ozeritskii, “On approximate projecting on a stable manifold”, Zh. Vychisl. Mat. Mat. Fiz., 45:9 (2005), 1580–1586; Comput. Math. Math. Phys., 45:9 (2005), 1525–1530

Citation in format AMSBIB
\Bibitem{KorOze05}
\by A.~A.~Kornev, A.~V.~Ozeritskii
\paper On approximate projecting on a stable manifold
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2005
\vol 45
\issue 9
\pages 1580--1586
\mathnet{http://mi.mathnet.ru/zvmmf595}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2216069}
\zmath{https://zbmath.org/?q=an:1086.37014}
\transl
\jour Comput. Math. Math. Phys.
\yr 2005
\vol 45
\issue 9
\pages 1525--1530


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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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