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Second Conference on Numerical Analysis and Applications
June 11-15, 2000
University of Rousse
Rousse, Bulgaria

Organizers
Plamen Yalamov, Marcin Paprzycki, Lubin Vulkov

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The second order nonhomogeneous difference scheme for singularly perturbed ordinary differential equation
by
I.G. Belukhina
Moscow State University

\bf The second order difference schemes for convection-diffusion equation and adjoint equation \thanks{This work is supported by the Russian Foundation for Basic Research under Grant N~97-01-00797, N~99-01-01056}

The second order difference schemes for convection-diffusion equation and adjoint equation 1

I. G. Belukhina 2

Two-point boundary value problem for the singularly perturbed not self-adjoint ODE of the second order is considered. On the piecewise uniform grid of the same kind as Shishkin's grid the approximation of the equation by FEM with quadratic elements is constructed on one part of the grid and the intermediate points are excluded. The modified monotone Samarskii's scheme is used on the other part. The uniform with respect to \epsilon accuracy of O(N-2) in Lh\infty-norm is proved for this nonhomogeneous three-point scheme.

Footnotes:

1This work is supported by the Russian Foundation for Basic Research under Grant N 97-01-00797, N 99-01-01056

2 Faculty of Computational Mathematics and Cybernetics, Moscow State University, Vorobjovy Gory, Moscow 119899, Russia. e-mail: belukh@cs.msu.su

Date received: February 1, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caeb-77.