Commun. Comput. Phys.,
Spectral Methods for Resolving Spike Dynamics in the Geirer-Meinhardt Model
Michael McCourt 1*, Nicholas Dovidio 2, Michael Gilbert 31 Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA.
2 Department of Mathematics, Davidson College, North Carolina, USA.
3 Department of Mathematics and Physics, Colorado State University-Pueblo, Colorado, USA.
Received 23 December 2006; Accepted (in revised version) 5 July 2007
Available online 30 October 2007
The Gierer-Meinhardt reaction-diffusion model is analyzed using a spectral collocation method. This reaction-diffusion system is governed by activator and inhibitor concentrations. Initially, the system is considered in one dimension and then in two dimensions; numerical results are presented for both cases. The algorithmic complexity and accuracy are compared to those of a moving finite element method. Finally, observations are made concerning when to use the proposed spectral method as opposed to the established moving mesh method.AMS subject classifications: 65M70
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Key words: Spike dynamics, Gierer-Meinhardt model, spectral collocation.
Email: firstname.lastname@example.org (M. McCourt), email@example.com (N. Dovidio), firstname.lastname@example.org (M. Gilbert)