Technical report: numerical solution of linear reaction-diffusion processes on fixed domain: criteria for colonization / Nur Zuhaily Zulkefly, Hasanatuz Zawanah Md Rafie and Siti Aisyah Shamsul - Zulkefly, Nur Zuhaily; Md Rafie, Hasanatuz Zawanah; Shamsul, Siti Aisyah (2017)
The macroscopic pattern exhibited by bacterial colony depends on certain environmental parameters and it gives some clues about the coordinated colonization strategy followed by the community of cell. Mathematical models of such colonization pattern usually take the form of a reaction-diffusion partial differential equation (PDE) on fixed domain. This research presents a numerical solution of linear reaction-diffusion PDE on fixed domain. The solution is for a general class of one-dimensional linear reaction-diffusion process with interval of domain fixed on x = [O, 1]. The linear reaction-diffusion problem model is solved numerically via finite difference method implicitly which are Crank-Nicholson (C-N) and Backward time Central space (BTCS) approach and is verified with pdepe solver in MATLAB. Crank-Nicholson and Backward time Central space approach are chosen because the methods are unconditionally stable. Furthermore, this research paper also illustrates a delicate interplay between the diffusivity associated with the spreading density profile and the grow rate of the bacteria species. Alternating the balance between this two features leads to different outcomes in term of colonizes the entire length of fixed domain and the condense rate of cell concentration at a particular nodes of the domain.