High order schemes for reaction-diffusion singularly perturbed systems

Clavero, C. (Universidad de Zaragoza) ; Gracia, J.L. (Universidad de Zaragoza) ; Lisbona F.J. (Universidad de Zaragoza)

Resumen: In this paper we are interested in solving e¿ciently a singularly per-turbed linear system of di¿erential equations of reaction-di¿usion type. Firstly, anon–monotone ¿nite di¿erence scheme of HODIE type is constructed on a Shishkinmesh. The previous method is modi¿ed at the transition points such that an inversemonotone scheme is obtained. We prove that if the di¿usion parameters are equal itis a third order uniformly convergent method. If the di¿usion parameters are di¿er-ent some numerical evidence is presented to suggest that an uniformly convergentscheme of order greater than two is obtained. Nevertheless, the uniform errors arebigger and the orders of uniform convergence are less than in the case correspondingto equal di¿usion parameters.

Idioma: Inglés

Año: 2009

Publicado en: Lecture Notes in Computational Science and Engineering 69 (2009), 107-115
ISSN: 1439-7358

Tipo y forma: Artículo (Versión definitiva)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)