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Volume 3, Issue 3
Spectral Methods for Resolving Spike Dynamics in the Geirer-Meinhardt Model

Michael McCourt, Nicholas Dovidio & Michael Gilbert

Commun. Comput. Phys., 3 (2008), pp. 659-678.

Published online: 2008-03

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  • Abstract

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. 

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@Article{CiCP-3-659, author = {Michael McCourt, Nicholas Dovidio and Michael Gilbert}, title = {Spectral Methods for Resolving Spike Dynamics in the Geirer-Meinhardt Model}, journal = {Communications in Computational Physics}, year = {2008}, volume = {3}, number = {3}, pages = {659--678}, abstract = {

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. 

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7869.html} }
TY - JOUR T1 - Spectral Methods for Resolving Spike Dynamics in the Geirer-Meinhardt Model AU - Michael McCourt, Nicholas Dovidio & Michael Gilbert JO - Communications in Computational Physics VL - 3 SP - 659 EP - 678 PY - 2008 DA - 2008/03 SN - 3 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7869.html KW - AB -

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. 

Michael McCourt, Nicholas Dovidio and Michael Gilbert. (2008). Spectral Methods for Resolving Spike Dynamics in the Geirer-Meinhardt Model. Communications in Computational Physics. 3 (3). 659-678. doi:
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