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Trudy Inst. Mat. i Mekh. UrO RAN, 2012, Volume 18, Number 2, Pages 80–91 (Mi timm810)  

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

Difference fitting scheme for a singularly perturbed problem with 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 turning point is considered. The solution has two exponential type boundary layers of different orders in neighborhoods of boundary points. 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 to the solution of the original differential problem as the grid step tends to zero.

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

Full text: PDF file (185 kB)
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Document Type: Article
UDC: 517.9
Received: 28.12.2011

Citation: K. V. Emel'yanov, “Difference fitting scheme for a singularly perturbed problem with turning point”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 2, 2012, 80–91

Citation in format AMSBIB
\Bibitem{Eme12}
\by K.~V.~Emel'yanov
\paper Difference fitting scheme for a~singularly perturbed problem with turning point
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2012
\vol 18
\issue 2
\pages 80--91
\mathnet{http://mi.mathnet.ru/timm810}
\elib{http://elibrary.ru/item.asp?id=17736188}


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    This publication is cited in the following articles:
    1. A. I. Korotkii, N. A. Artemova, N. A. Vaganova, O. O. Kovrizhnykh, L. I. Rubina, O. N. Ulyanov, O. V. Ushakova, M. Yu. Filimonov, I. A. Tsepelev, “O razrabotkakh analiticheskikh i chislennykh metodov resheniya zadach mekhaniki sploshnoi sredy”, Tr. IMM UrO RAN, 19, no. 2, 2013, 203–215  mathnet  mathscinet  elib
    2. K. V. Emelyanov, “O raznostnoi skheme pervogo poryadka tochnosti dlya singulyarno vozmuschennoi zadachi s tochkoi povorota”, Tr. IMM UrO RAN, 19, no. 3, 2013, 120–135  mathnet  mathscinet  elib
  • Trudy Instituta Matematiki i Mekhaniki UrO RAN
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