Asymptotic behaviour for a numerical approximation of a parabolic problem with blowing up solutions
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...
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| Autores principales: | , |
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| Formato: | JOUR |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_03770427_v135_n1_p135_Groisman |
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| Sumario: | 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. |
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