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Pregled bibliografske jedinice broj: 446403

Časopis

Autori: Kavčič, Iva; Rogina, Mladen; Bosner, Tina
Naslov: Singularly perturbed advection-diffusion-reaction problems : Comparison of operator-fitted methods
( Singularly perturbed advection-diffusion-reaction problems : Comparison of operator-fitted methods )
Izvornik: Mathematics and computers in simulation (0378-4754) 81 (2011), 10; 2215-2224
Vrsta rada: članak
Ključne riječi: singular perturbations; boundary layers; collocation; difference schemes; exponential splines
( singular perturbations; boundary layers; 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{; ; ; ; \left(\pm p x\right)}; ; ; ; \}; ; ; ; $ 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{; ; ; ; \left(p x\right)}; ; ; ; \}; ; ; ; $, 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.
Projekt / tema: 037-1193086-2771
Izvorni jezik: eng
Rad je indeksiran u
bazama podataka:
Current Contents Connect (CCC)
Scopus
SCI-EXP, SSCI i/ili A&HCI
Science Citation Index Expanded (SCI-EXP) (sastavni dio Web of Science Core Collectiona)
Kategorija: Znanstveni
Znanstvena područja:
Matematika,Fizika,Geologija
URL Internet adrese: http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6V0T-51TYF2P-3-1&_cdi=5655&_user=3875467&_pii=S0378475410004313&_origin=browse&_coverDate=06%2F30%2F2011&_sk=999189989&view=c&wchp=dGLzVlb-zSkWA&md5=bae1cf9d4c1660fe7ddd9b728a3b6021&ie=/sdarticle.pdf
http://www.sciencedirect.com/science/article/pii/S0378475410004313
Broj citata:
Altmetric:
DOI: 10.1016/j.matcom.2010.12.029
URL cjelovitog teksta:
Google Scholar: Singularly perturbed advection-diffusion-reaction problems : Comparison of operator-fitted methods
Upisao u CROSBI: ikavcic@geolpmf.hr (ikavcic@geolpmf.hr), 3. Ožu. 2010. u 12:29 sati
Napomene:
Rad je prezentiran na skupu The 3rd International Conference on Approximation Methods and Numerical Modeling in Environment and Natural Resources (MAMERN 2009).



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