Numerical methods for a nonlinear reaction-diffusion system modelling a batch culture of biofilm

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• 作者：Eva Balsa-Canto^a ; ^{ebalsa@iim.csic.es} ; Alejandro Ló ; pez-Nú ; ñ ; ez^b ; ^{alopeznu@gmail.com} ; Carlos Vá ; zquez ; ^b ; ^{carlosv@udc.es}
• 关键词：Biofilms ; continuum models ; Nonlinear reaction&ndash ; diffusion equations ; Numerical methods ; Crank&ndash ; Nicolson
• 刊名：Applied Mathematical Modelling
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：41
• 期：Complete
• 页码：164-179
• 全文大小：6042 K
• 卷排序：41

文摘

A biofilm model is formulated by a quasilinear reaction–diffusion system of equations. It exhibits possible degeneracy and singularities in the diffusion coefficient. An original combination of Crank–Nicolson and Newton methods speed up computations. Numerical tests show the expected behaviour of biomass and nutrients concentrations. Numerical results also illustrate some theoretically proved qualitative properties.