The Gierer-Meinhardt reaction-diffusion model is analyzed using a spectralcollocation method. This reaction-diffusion system is governed by activator and inhibitorconcentrations. Initially, the system is considered in...The Gierer-Meinhardt reaction-diffusion model is analyzed using a spectralcollocation method. This reaction-diffusion system is governed by activator and inhibitorconcentrations. Initially, the system is considered in one dimension and thenin two dimensions;numerical results are presented for both cases. The algorithmiccomplexity and accuracy are compared to those of a moving finite element method.Finally, observations are made concerning when to use the proposed spectral methodas opposed to the established moving mesh method.展开更多
基金the NSF Grant DMS-0453600.Special thanks are due to the Hong Kong Baptist University for their generous accommodations,specifically Dr.Tao Tang for his time and support.Also we would like to thank Dr.Graeme Fairweather for his guidance throughout this project,and Dr.Greg Fasshauer for his suggestions and contributions.
文摘The Gierer-Meinhardt reaction-diffusion model is analyzed using a spectralcollocation method. This reaction-diffusion system is governed by activator and inhibitorconcentrations. Initially, the system is considered in one dimension and thenin two dimensions;numerical results are presented for both cases. The algorithmiccomplexity and accuracy are compared to those of a moving finite element method.Finally, observations are made concerning when to use the proposed spectral methodas opposed to the established moving mesh method.
