15. ÖMG-Kongress
Jahrestagung der Deutschen Mathematikervereinigung

16. bis 22. September 2001 in Wien


Sektion 11 - Numerische Mathematik, Wissenschaftliches Rechnen
Freitag, 21. September 2001, 16.30, Hörsaal 47

 

On an Uniformly Convergent Spline Difference Scheme

Ljiljana Pavlovic, University of Novi Sad (Koautor: Zorica Uzelac)

 

We derive an $ \varepsilon$-uniform numerical method for a convection-diffusion boundary value problem given by the equation

$\displaystyle \varepsilon y''(x) + p(x)y'(x) = f(x) \quad x\in (0,1), \qquad
y(0) = 0, \; \; \; y(1) = 0,
$

where $ 0< \varepsilon \ll 1.$ Our method is based on a collocation with quadratic spline as an approximation function. The collocation points are defined by non-uniform mesh of Bakhvalov and Shishkin type [1], [2]. Numerical results which demonstrate the effectiveness of the method are presented.

[1] N. S. Bakhvalov, ``On optimization of methods to slove boundary value problems with boundary layers'', Zh. Vychisl. Mat. Mat. Fiz. 9, (1969), 841-859
[2] P. A. Farrell, A. F. Hegarty, J. J. H. Miller, E. O'Riordan, G. I. Shishkin, ``Robust Computational Techniques for Boundary Layers'', CRC Press LLC, (2000)

E-Mail: ljiljap@eunet.yu


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