Geodesic
On approximate projecting on a stable manifold
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 9, pp. 1580-1586

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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. 
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     author = {A. A. Kornev and A. V. Ozeritskii},
     title = {On approximate projecting on a stable manifold},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1580--1586},
     publisher = {mathdoc},
     volume = {45},
     number = {9},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_9_a5/}
}
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A. A. Kornev; A. V. Ozeritskii. On approximate projecting on a stable manifold. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 9, pp. 1580-1586. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_9_a5/