Full discretization of some reaction diffusion equation with blow up

Geneviève Barro; Benjamin Mampassi; Longin Some; Jean Ntaganda; Ousséni So

Open Mathematics (2006)

  • Volume: 4, Issue: 2, page 260-269
  • ISSN: 2391-5455

Abstract

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This paper aims at the development of numerical schemes for nonlinear reaction diffusion problems with a convection that blows up in a finite time. A full discretization of this problem that preserves the blow - up property is presented as well as a numerical simulation. Efficiency of the method is derived via a numerical comparison with a classical scheme based on the Runge Kutta scheme.

How to cite

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Geneviève Barro, et al. "Full discretization of some reaction diffusion equation with blow up." Open Mathematics 4.2 (2006): 260-269. <http://eudml.org/doc/268920>.

@article{GenevièveBarro2006,
abstract = {This paper aims at the development of numerical schemes for nonlinear reaction diffusion problems with a convection that blows up in a finite time. A full discretization of this problem that preserves the blow - up property is presented as well as a numerical simulation. Efficiency of the method is derived via a numerical comparison with a classical scheme based on the Runge Kutta scheme.},
author = {Geneviève Barro, Benjamin Mampassi, Longin Some, Jean Ntaganda, Ousséni So},
journal = {Open Mathematics},
keywords = {65M06; 65N22},
language = {eng},
number = {2},
pages = {260-269},
title = {Full discretization of some reaction diffusion equation with blow up},
url = {http://eudml.org/doc/268920},
volume = {4},
year = {2006},
}

TY - JOUR
AU - Geneviève Barro
AU - Benjamin Mampassi
AU - Longin Some
AU - Jean Ntaganda
AU - Ousséni So
TI - Full discretization of some reaction diffusion equation with blow up
JO - Open Mathematics
PY - 2006
VL - 4
IS - 2
SP - 260
EP - 269
AB - This paper aims at the development of numerical schemes for nonlinear reaction diffusion problems with a convection that blows up in a finite time. A full discretization of this problem that preserves the blow - up property is presented as well as a numerical simulation. Efficiency of the method is derived via a numerical comparison with a classical scheme based on the Runge Kutta scheme.
LA - eng
KW - 65M06; 65N22
UR - http://eudml.org/doc/268920
ER -

References

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  1. [1] H. Amann: “On the existence of positive solutions of nonlinear elliptic boundary value problems”, Indiana Univ. Math. J., Vol. 21, (1971), p. 125. http://dx.doi.org/10.1512/iumj.1971.21.21012 
  2. [2] M. Chlebik and M. Fila: “Blow-up of positive solutions of a semilinear parabolic equation with a gradient term.”, Dyn. Contin. Discrete Impulsive Syst., Vol. 10, (2003), pp. 525–537. Zbl1028.35071
  3. [3] V.A. Galaktionov and J.L. Vàzquez: “The problem of blow-up in nonlinear parabolic equations”, Discrete Cont. Dyn. S., Vol 8(2), (2002). Zbl1010.35057
  4. [4] M.N. Le Roux: “Numerical solution of fast or slow diffusion equations”, J. Comput. Appl. Math., Vol. 97, (1998), pp. 121–136. Zbl0932.65101
  5. [5] M.N. Le Roux: “Semidiscretization in time of nonlinear parabolic equations with blow up of the solution”, Siam J. Numer. Anal., Vol. 31, (1994), pp. 170–195. Zbl0803.65095
  6. [6] M.N. Le Roux and H. Wilhelmsson: “Simultaneous diffusion, reaction and radiative loss processes in plasmas: numerical analysis with application to the dynamics of a fusion reactor plasma”, Phys. Scripta, Vol. 45, (1992), pp. 188–192. 

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