Journal
JOURNAL OF MATHEMATICAL CHEMISTRY
Volume 56, Issue 1, Pages 30-68Publisher
SPRINGER
DOI: 10.1007/s10910-017-0779-z
Keywords
Reaction-diffusion; Method of lines; Reaction networks
Funding
- NSF [DMS-1600272, DMS-1517577]
- Simons Foundation [246063]
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We show that solutions of the chemical reaction-diffusion system associated to in one spatial dimension can be approximated in on any finite time interval by solutions of a space discretized ODE system which models the corresponding chemical reaction system replicated in the discretization subdomains where the concentrations are assumed spatially constant. Same-species reactions through the virtual boundaries of adjacent subdomains lead to diffusion in the vanishing limit. We show convergence of our numerical scheme by way of a consistency estimate, with features generalizable to reaction networks other than the one considered here, and to multiple space dimensions. In particular, the connection with the class of complex-balanced systems is briefly discussed here, and will be considered in future work.
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