Full discretization of some reaction diffusion equation with blow up

• Autorzy: Geneviève Barro , Benjamin Mampassi , Longin Some , Jean Ntaganda , Ousséni So
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Full discretization; Runge Kutta scheme; reaction diffusion equation; nonlinear parabolic problems; blow-up; 65M06; 65N22

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2006
• Tom: 4
• Numer: 2
• Strony: 260-269

Daty

wydano

2006-06-01

online

2006-06-01

Twórcy

autor

Geneviève Barro

• Université de Ouagadougou

autor

Benjamin Mampassi

• Université Cheikh Anta Diop

autor

Longin Some

• Université de Ouagadougou

autor

Jean Ntaganda

• Université Cheikh Anta Diop

autor

Ousséni So

• Université de Ouagadougou

Bibliografia

• [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] 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.
• [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).
• [4] M.N. Le Roux: “Numerical solution of fast or slow diffusion equations”, J. Comput. Appl. Math., Vol. 97, (1998), pp. 121–136.
• [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.
• [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.

Identyfikatory

DOI

10.1007/s11533-006-0002-0