TY - JOUR T1 - Spectral Methods for Resolving Spike Dynamics in the Geirer-Meinhardt Model 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.