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 Zh. Vychisl. Mat. Mat. Fiz., 1990, Volume 30, Number 5, Pages 716–726 (Mi zvmmf3265)

Numerical solution of a quasilinear parabolic equation with a boundary layer

I. P. Boglaev

Moscow

Abstract: To solve a quasilinear parabolic equation with small parameter multiplying the derivatives with respect to the spatial variables, a numerical method is constructed with an estimate of the error, which is uniform with respect to the parameter. The construction of a nonlinear difference scheme is based on the method of straight lines and on the application of exact systems to one-dimensional problems. The computational mesh is chosen so that its density increases in a suitable way in the neighbourhood of the boundary. We propose that the nonlinear scheme be solved by an iterative algorithm, which converges uniformly with respect to the small parameter.

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English version:
USSR Computational Mathematics and Mathematical Physics, 1990, 30:3, 55–63

Bibliographic databases:

UDC: 519.633
MSC: Primary 65M20; Secondary 65M50, 65M06, 35R35, 35K55, 35B25
Revised: 09.06.1989

Citation: I. P. Boglaev, “Numerical solution of a quasilinear parabolic equation with a boundary layer”, Zh. Vychisl. Mat. Mat. Fiz., 30:5 (1990), 716–726; U.S.S.R. Comput. Math. Math. Phys., 30:3 (1990), 55–63

Citation in format AMSBIB
\Bibitem{Bog90} \by I.~P.~Boglaev \paper Numerical solution of a~quasilinear parabolic equation with a~boundary layer \jour Zh. Vychisl. Mat. Mat. Fiz. \yr 1990 \vol 30 \issue 5 \pages 716--726 \mathnet{http://mi.mathnet.ru/zvmmf3265} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1058619} \zmath{https://zbmath.org/?q=an:0705.65067} \transl \jour U.S.S.R. Comput. Math. Math. Phys. \yr 1990 \vol 30 \issue 3 \pages 55--63 \crossref{https://doi.org/10.1016/0041-5553(90)90190-4}