Method of Lines Analysis of Turing Models

Schiesser examines the numerical integration, or solution, of a system of partial differential equations that describe a combination of chemical reaction and diffusion, that is, reaction-diffusion PDEs, which correspond to a system that British mathematician Alan Turing (1912-54) discussed, and is therefore known as a Turing model. Specifically, he says, Turing considered how a reaction-diffusion system can be formulated that does not have the usual smoothing properties of a diffusion or dispersion system, and can, in fact, develop a spatial pattern or variation that might be interpreted as a form of morphogenesis. This is not a formal mathematical presentation with theorems and proofs, he says, but a selection of examples along with details for computing numerical solutions, particularly with documented, transportable source code in R. Annotation ©2017 Ringgold, Inc., Portland, OR (protoview.com)