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Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2015, Volume 157, Book 1, Pages 60–74 (Mi uzku1294)  

Investigation of a two-grid method of improved accuracy for the elliptic reaction–diffusion equation with boundary layers

S. V. Tikhovskaya

Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Omsk, Russia

Abstract: A two-grid method for the elliptic equation with a small parameter $\varepsilon$ multiplying the highest derivative is investigated. The $\varepsilon$-uniformly convergent difference scheme on the Shishkin mesh is considered. To resolve the difference scheme, a two-grid method with $\varepsilon$-uniform interpolation formula is used. To increase the accuracy of the scheme, the Richardson extrapolation in the two-grid method is applied. The results of numerical experiments are discussed. Various iterative methods for implementation of the two-grid algorithm are suggested.

Keywords: elliptic reaction–diffusion equation, singular perturbation, Shishkin mesh, two-grid method, Richardson extrapolation, uniform convergence.

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UDC: 519.63
Received: 23.01.2015

Citation: S. V. Tikhovskaya, “Investigation of a two-grid method of improved accuracy for the elliptic reaction–diffusion equation with boundary layers”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 157, no. 1, Kazan University, Kazan, 2015, 60–74

Citation in format AMSBIB
\Bibitem{Tik15}
\by S.~V.~Tikhovskaya
\paper Investigation of a~two-grid method of improved accuracy for the elliptic reaction--diffusion equation with boundary layers
\serial Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
\yr 2015
\vol 157
\issue 1
\pages 60--74
\publ Kazan University
\publaddr Kazan
\mathnet{http://mi.mathnet.ru/uzku1294}
\elib{http://elibrary.ru/item.asp?id=23465301}


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