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 Trudy Inst. Mat. i Mekh. UrO RAN, 2013, Volume 19, Number 3, Pages 120–135 (Mi timm969)

On a first-order accurate difference scheme for a singularly perturbed problem with a turning point

K. V. Emel'yanov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: A singularly perturbed problem with a turning point is considered. The solution has a boundary layer of exponential type in a neighborhood of a boundary point. The problem is solved approximately by means of a difference scheme of exponential fitting on a uniform grid. It is proved that the solutions obtained from this scheme converge uniformly with respect to the perturbation parameter with the first order of accuracy to the solution of the original differential problem as the grid step tends to zero.

Keywords: singularly perturbed problem for a second-order ordinary differential equation, asymptotic expansion, difference scheme.

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Bibliographic databases:
UDC: 517.9

Citation: K. V. Emel'yanov, “On a first-order accurate difference scheme for a singularly perturbed problem with a turning point”, Trudy Inst. Mat. i Mekh. UrO RAN, 19, no. 3, 2013, 120–135

Citation in format AMSBIB
\Bibitem{Eme13} \by K.~V.~Emel'yanov \paper On a~first-order accurate difference scheme for a~singularly perturbed problem with a~turning point \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2013 \vol 19 \issue 3 \pages 120--135 \mathnet{http://mi.mathnet.ru/timm969} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3363304} \elib{http://elibrary.ru/item.asp?id=20234978}