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

Michael McCourt, Nicholas Dovidio & Michael Gilbert

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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://dor.org/ UR - https://global-sci.org/intro/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 & Michael Gilbert. (1970). Spectral Methods for Resolving Spike Dynamics in the Geirer-Meinhardt Model. Communications in Computational Physics. 3 (3). 659-678. doi:
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