Discretization of the Cauchy problem for a fast diffusion equation

Authors:
Paul-Emile Maingé
Affiliations:
Département Scientifique Interfacultaire, GRIMMAG, Université des Antilles-Guyane, Campus de Schoelcher, 97230 Cedex, Martinique, France
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

Citing 6
Cited 0

solution of nonlinear diffusion problems by linear approximation schemes

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Numerical solution of a fast diffusion equation

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Abstract

In this paper, we propose and study a fully discretization for computing the positive and (possibly) blowing-up solution of the Cauchy problem: u"t-@?"x^2u^m=@au^p^"^1 in R, where m@?(0,1), p"11, @a0, with an initial condition u"0 assumed to be a nonnegative and continuous function with compact support. The convergence of the numerical method is proved.