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The highest-order schemes for singularly perturbed problems
by
Boris M. Bagaev
Siberian Aerospace Academy, Krasnoyarsk, Russia
Coauthors: Vladimir V. Shaidurov (Institute of Computational Modelling, Russian Academy of Sciences, Krasnoyarsk)
The ways for improving the accuracy of approximate solutions of mathematical physics problems are considered in several directions. Among them are a simple method to raise the accuracy of difference schemes connected with decreasing the intervals of discretization of differential problems, and also the use of multipoint difference schemes and correction by high-order differences, and Richardson's extrapolational method with using the sequence of meshes, and many others.
The difference schemes constructed in this work concern to the class of compact difference schemes. The difference schemes are are said to be compact if they have the highest order of accuracy but are written out on the stencil unessentially differing from traditional one for the given equation. Usually these are schemes with the third or fourth order of approximation.
Another case is the application of these schemes to singularly perturbed problems which are characterized by growth of the derivatives of the solution in some boundary region. The given method is applied to problems which have ordinary regular boundary layers, either parabolic or elliptic layers.
Date received: February 26, 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 # caen-40.