Naslov
Comparison of Operator-Fitted methods for Singularly Perturbed Advection-Diffusion-Reaction Problems

Autori
Kavčič, Iva ; Rogina, Mladen ; Bosner, Tina

Vrsta, podvrsta i kategorija rada
Radovi u zbornicima skupova, cjeloviti rad (in extenso), znanstveni

Izvornik
Proceedings of the 3rd International Conference on Approximation Methods and numerical Modeling in Environment and Natural Resources (MAMERN 2009) / Amaziane, B. ; Barrera D. ; Fortes M. A. ; Ibanez, M. J. ; Odunlami, M. ; Palomares, A. ; Pasadas, M. ; Rodriguez M. L. ; Sbibih, D. - Granada : Imprenta Comercial. Motril. Granada, 2009, 2215-2224

ISBN
978-84-338-5006-5

Skup
3rd International Conference on Approximation Methods and numerical Modeling in Environment and Natural Resources (MAMERN 2009)

Mjesto i datum
Pau, Francuska, 08.06.2009. - 11.06.2009

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Singular perturbations ; collocation ; difference schemes ; exponential splines

Sažetak
We compare classical methods for singular perturbation problems, such as El-Mistikawy and Werle scheme and its modifications, to exponential spline collocation schemes. We discuss subtle differences that exist in applying this method to one dimensional reaction–diffusion problems and advection–diffusion problems. For pure advection–diffusion problems, exponential tension spline collocation is less capable of capturing only one boundary layer, which happens when no reaction term is present. Thus the existing collocation scheme in which the approximate solution is a projection to the space piecewisely spanned by {; ; 1, x, exp (± px)}; ; is inferior to the generalization of El-Mistikawy and Werle method proposed by Ramos. We show how to remedy this situation by considering projections to spaces locally spanned by {; ; 1, x, x2, exp (px)}; ; , where p > 0 is a tension parameter. Next, we exploit a unique feature of collocation methods, that is, the existence of special collocation points which yield better global convergence rates and double the convergence order at the knots.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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