Higham, D.J. and Owren, B. (1996) Non-normality effects in a discretised, nonlinear, reaction-convection-diffusion equation. Journal of Computational Physics, 124 (2). pp. 309-323. ISSN 0021-9991Full text not available in this repository. (Request a copy from the Strathclyde author)
What is the long-time effect of adding convention to a discretised reaction-diffusion equation? For linear problems, it is well known that convection may denormalise the process, and, in particular, eigenvalue-based stability predictions may be overoptimistic. This work deals with a related issue - with a nonlinear reaction term, the nonnormality can greatly influence the long-time dynamics. For a nonlinear model problem with Dirichlet boundary conditions, it is shown that the basin of attraction of the 'correct' steady state can be shrunk in a directionally biased manner. A normwise analysis provides lower bounds on the basin of attraction and a more revealing picture is provided by pseudo-eigenvalues. In extreme cases, the computed solution can converge to a spurious, bounded, steady state that exists only in finite precision arithmetic. The impact of convection on the existence and stability of spurious, periodic solutions is also quantified.
|Keywords:||discretised reaction-diffusion equation, linear problems, differential equations, mathematics, Dirichlet boundary, convection, Mathematics, Physics and Astronomy (miscellaneous), Computer Science Applications|
|Subjects:||Science > Mathematics|
|Department:||Faculty of Science > Mathematics and Statistics|
|Depositing user:||Ms Sarah Scott|
|Date Deposited:||01 Mar 2006|
|Last modified:||22 Mar 2017 09:03|