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Abstract:

In this paper, we study the asymptotic behaviour of a semidiscrete numerical approximation for Ut = Uxx + up in a bounded interval, (0, 1), with Dirichlet boundary conditions. We focus in the behaviour of blowing up solutions. We find that the blow-up rate for the numerical scheme is the same as for the continuous problem. Also we find the blow-up set for the numerical approximations and prove that it is contained in a neighbourhood of the blow-up set of the continuous problem when the mesh parameter is small enough. © 2001 Elsevier Science B.V. All rights reserved.

Registro:

Documento: Artículo
Título:Asymptotic behaviour for a numerical approximation of a parabolic problem with blowing up solutions
Autor:Groisman, P.; Rossi, J.D.
Filiación:Departamento de Matemática, F.C.E y N., UBA, 1428 Buenos Aires, Argentina
Palabras clave:Asymptotic behaviour; Blow-up; Semidiscretization in space; Semilinear parabolic equations; Asymptotic stability; Boundary conditions; Semidiscrete numerical approximation; Approximation theory; mathematical analysis
Año:2001
Volumen:135
Número:1
Página de inicio:135
Página de fin:155
DOI: http://dx.doi.org/10.1016/S0377-0427(00)00571-9
Título revista:Journal of Computational and Applied Mathematics
Título revista abreviado:J. Comput. Appl. Math.
ISSN:03770427
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03770427_v135_n1_p135_Groisman

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Citas:

---------- APA ----------
Groisman, P. & Rossi, J.D. (2001) . Asymptotic behaviour for a numerical approximation of a parabolic problem with blowing up solutions. Journal of Computational and Applied Mathematics, 135(1), 135-155.
http://dx.doi.org/10.1016/S0377-0427(00)00571-9
---------- CHICAGO ----------
Groisman, P., Rossi, J.D. "Asymptotic behaviour for a numerical approximation of a parabolic problem with blowing up solutions" . Journal of Computational and Applied Mathematics 135, no. 1 (2001) : 135-155.
http://dx.doi.org/10.1016/S0377-0427(00)00571-9
---------- MLA ----------
Groisman, P., Rossi, J.D. "Asymptotic behaviour for a numerical approximation of a parabolic problem with blowing up solutions" . Journal of Computational and Applied Mathematics, vol. 135, no. 1, 2001, pp. 135-155.
http://dx.doi.org/10.1016/S0377-0427(00)00571-9
---------- VANCOUVER ----------
Groisman, P., Rossi, J.D. Asymptotic behaviour for a numerical approximation of a parabolic problem with blowing up solutions. J. Comput. Appl. Math. 2001;135(1):135-155.
http://dx.doi.org/10.1016/S0377-0427(00)00571-9