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Zeitschrift für Analysis und ihre Anwendungen


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Volume 12, Issue 4, 1993, pp. 723–728
DOI: 10.4171/ZAA/534

Published online: 1993-12-31

A Higher Order Uniform Convergence Result for a Turning Point Problem

H.-G. Roos[1] and R. Vulanović[2]

(1) Technische Universität Dresden, Germany
(2) University Novi Sad, Serbia

We describe a new fitted scheme, of $k$-th order uniform accuracy with arbitrary $k$, for a turning point problem of cusp type. The scheme is constructed by applying an iterative technique to an auxiliary problem obtained after replacing coefficient functions in the original problem by piecewise polynomials. The analysis of the scheme is based on an improved stability result.

Keywords: Singular perturbations, boundary value problems, turning points, higher order schemes

Roos H.-G., Vulanović R.: A Higher Order Uniform Convergence Result for a Turning Point Problem. Z. Anal. Anwend. 12 (1993), 723-728. doi: 10.4171/ZAA/534