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We show that solutions of the chemical reaction-diffusion system associatedto $A+B\rightleftharpoons C$ in one spatial dimension can be approximated in$L^2$ on any finite time interval by solutions of a space discretized ODEsystem which models the corresponding chemical reaction system replicated inthe discretization subdomains where the concentrations are assumed spatiallyconstant. Same-species reactions through the virtual boundaries of adjacentsubdomains lead to diffusion in the vanishing limit. We show convergence of ournumerical scheme by way of a consistency estimate, with features generalizableto reaction networks other than the one considered here, and to multiple spacedimensions. In particular, the connection with the class of complex-balancedsystems is briefly discussed here, and will be considered in future work.

Chemical reaction-diffusion networks; convergence of the method of lines