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


Kavčič, Iva; Rogina, Mladen; Bosner, Tina
Comparison of Operator– Fitted methods for Singularly Perturbed Advection– Diffusion– Reaction Problems // 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. (ur.).
Granada, Španjolska: Imprenta Comercial. Motril. Granada, 2009. str. 521-525 (predavanje, međunarodna recenzija, cjeloviti rad (in extenso), znanstveni)


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, Španjolska : Imprenta Comercial. Motril. Granada, 2009, 521-525

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, 08-11.06.2009

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Singular perturbations; collocation; difference schemes; exponential splines
(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 reaction– diffusion problems and advection– diffusion problems. If the advection– diffusion– reaction problem is specified in such a way that two boundary internal layers exist, collocation method is incapable 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, x^2, 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



POVEZANOST RADA


Projekt / tema
037-1193086-2771 - Numeričke metode u geofizičkim modelima (Saša Singer, )

Ustanove
Prirodoslovno-matematički fakultet, Matematički odjel, Zagreb,
Prirodoslovno-matematički fakultet, Zagreb