Non-normality effects in a discretised, nonlinear, reaction-convection-diffusion equation
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 0021-9991
Full text not available in this repository.Request a copy from the Strathclyde authorAbstract
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.
ORCID iDs
Higham, D.J.
Item type: Article ID code: 192 Dates: DateEvent15 March 1996PublishedKeywords: 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: 20 Jan 2021 16:42 URI: https://strathprints.strath.ac.uk/id/eprint/192