Numerical Solution of Nonlinear Reaction Diffusion Processes

In this paper, the author considers a nonlinear reaction diffusion equation, i.e., a nonlinear heat equation with a source term. The solution of this equation may blow up in a finite time. A scheme for the discretization in time of that problem is proposed, and the same sufficient condition of a blo...

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Bibliographic Details
Published in:SIAM journal on numerical analysis 2000, Vol.37 (5), p.1644-1656
Main Author: Le Roux, Marie-Noelle
Format: Article
Language:English
Subjects:
Boundary value problems
Differential equations
Eigenvalues
Exact sciences and technology
Inequality
Mathematical analysis
Mathematical sequences
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Plasma density
Plasma diffusion
Plasma temperature
Reaction diffusion equations
Roux
Sciences and techniques of general use
Sufficient conditions
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Summary:In this paper, the author considers a nonlinear reaction diffusion equation, i.e., a nonlinear heat equation with a source term. The solution of this equation may blow up in a finite time. A scheme for the discretization in time of that problem is proposed, and the same sufficient condition of a blowup is obtained for the numerical solution as for the exact solution. The stability and the convergence of the scheme is proved.
ISSN:0036-1429
1095-7170
DOI:10.1137/S0036142998335996