Richardson extrapolation for a singularly perturbed turning point problem with exponential boundary layers

We consider an interior turning point problem with two exponential boundary layers. Its discretisation on a piecewise-uniform Shishkin mesh yields a scheme which is uniformly convergent (measured in the discrete maximum norm) of almost order one. Richardson extrapolation improves the accuracy to O(N...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2015-12, Vol.290, p.334-351
Main Authors: Becher, S., Roos, H.-G.
Format: Article
Language:English
Subjects:
Accuracy
Boundary layer
Computation
Error expansion
Extrapolation
Mathematical models
Norms
Richardson extrapolation
Shishkin mesh
Singularly perturbed turning point problem
Turning
Upwind scheme
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Summary:We consider an interior turning point problem with two exponential boundary layers. Its discretisation on a piecewise-uniform Shishkin mesh yields a scheme which is uniformly convergent (measured in the discrete maximum norm) of almost order one. Richardson extrapolation improves the accuracy to O(N−2ln2N). Both can be proved under the assumption ε≤CN−1.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2015.05.022